Discrete Mathematics Functions Questions And Answers

1) The set x is ____________ if it consists of an integer that is neither positive nor negative and is a set.

  1. The Set is a Finite Set.
  2. The set is an Empty set
  3. The set is a Non-empty set
  4. The Set is both Non- empty set and a Finite set.

Answer: The Set is both Non- empty set and a Finite set.

Explanation:

Set 0 is the non-empty, finite set.


2) X is in the ________ set if x N and x is a prime number.

  1. Infinite set
  2. Not a set
  3. Finite set
  4. Empty set

Answer: Infinite set

Explanation:

Since there is no extreme prime, there are an endless amount of primes.


3) If x is a set and there is an actual number in the range of 1 to 2 in the set, the set is called ________.

  1. Empty set
  2. Finite set
  3. Infinite set
  4. None of the mentioned

Answer: Infinite set.

Explanation:

Infinite real numbers between 1 and 2 make up the infinite set X.


4) Which of the following is a subset of set {1, 2, 3, 4}?

  1. {1, 2}
  2. {1, 2, 3}
  3. {1}
  4. All of the mentioned

Answer: All of the mentioned


5) If set x contains a positive prime integer that divides 72, convert the set to roster form.

  1. {∅}
  2. {3, 5, 7}
  3. {2, 3}
  4. {2, 3, 7}

Answer: {2, 3}

Explanation:

Two and three are the prime divisors of 72. The roster form for set x is therefore (2, 3).


6) The exact subset of the power set of an empty or Null set is _________.

  1. Two
  2. One
  3. Zero
  4. Three

Answer: One

Explanation: The only member of the Null set's power set is the empty set.


7) What is the Cartesian product of sets A and B, where A = 1, 2 and B = a, b, respectively?

  1. { (1, a), (1, b), (2, a), (b, b) }
  2. { (1, 1), (a, a), (2, a), (1, b) }
  3. { (1, 1), (2, 2), (a, a), (b, b) }
  4. { (1, a), (2, a), (1, b), (2, b) }

Answer: { (1, a), (2, a), (1, b), (2, b) }

Explanation:

A subset R of the Cartesian product A x B is a relation from set A to set B.


8) The individuals that make up the set S = x |, in where x is an integer square, are x 100.

  1. {0, 2, 4, 5, 9, 55, 46, 49, 99, 81}
  2. {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
  3. {1, 4, 9, 16}
  4. {0, 1, 4, 9, 25, 36, 49, 123}

Answer: {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

Explanation:

The set S contains the square of any number less than 10. The third option is therefore the best one given the alternatives.


9) The set _____________ is the intersection of the sets 1, 2, 8, 9, 10, 5 and 1, 2, 6, 10, 12.

  1. {5, 6, 12, 15}
  2. {1, 2, 10}
  3. {2, 5, 10, 9}
  4. {1, 6, 12, 9, 8}

Answer: {1, 2, 10}

Explanation:

The intersection of the two sets is the set that holds the elements that are shared by the two given sets. As a result, the first option is the best one given the sets that are given.


10) The set of numbers between 1, 2, 5, 6, and 3, 6, 8, is the difference.

  1. {3, 8}
  2. {1, 3}
  3. {5, 6, 8}
  4. {2, 6, 5}

Answer: {3, 8}

Explanation:

The set that contains the items that are in set A but not in set B is known as the "difference between the sets A and B" (A-B).


11) What is n(A B) if n(A) = 20, n(B) = 30, and n(A U B) = 40?

  1. 30
  2. 20
  3. 40
  4. 10

Answer: 10

Explanation:

We may determine n(A B) using the formula, n(A U B) = n(A) + n(B) - n(A B).

n(A B) is equal to n(A) + n(B) - n(A U B).

Thus, n(A B) = 10 because n(A B) = 20 + 30 - 40.


12) Assuming there are 16 total players, divide the number of football players by 10, the number of cricket players only by 6, and the number of cricket players just by __________.

  1. 16
  2. 4
  3. 8
  4. 10

Answer: 4

Explanation:

None


13) What one of the following qualifies as a distinct object?

  1. Integers
  2. People
  3. Rational numbers
  4. All of the mentioned

Answer: All of the mentioned

Explanation:

People, homes, integers, rational numbers, and cars are examples of discrete objects.


14) Of the possibilities below, which one has two equal sets?

  1. X = {5, 6} and Y = {6}
  2. X = {5, 6, 9} and Y = {5, 6}
  3. X = {5, 6, 8, 9} and Y = {6, 8, 5, 9}
  4. X = {5, 6} and Y = {5, 6, 3}

Answer: X = {5, 6, 8, 9} and Y = {6, 8, 5, 9}

Explanation:

Given that the elements in both X and Y sets are the same, the second possibility is correct.


15) The cardinality of the power set in the set "1, 5, 6" is ______.

  1. 8
  2. 5
  3. 6
  4. 10

Answer: 8

Explanation:

Any set's power set is the collection of all of its subsets. As a result, P(1, 5, 6) = null, 1, 5, 1, 6, 5, 6, and 1, 5, 6. Eight elements make up the given set's power set. As a result, the cardinality of the provided set is 8.


16) Is the (Set Y) x (Set X) Cartesian product equivalent to the (Set X) x (Set Y) Cartesian product, or not?

  1. Yes
  2. No
  3. None of the above
  4. I don't know

Answer: No

Explanation:

The Cartesian product of (Set Y) x (Set X) and (Set X) x (Set Y) are not the same.

Assume X = 5, 6, and 7 and Y = a, b, and Cartesian products of (set X) x (set Y) are defined as (a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7), (c, 5), (c, 6), (c, 7), and (a, 5), (a, 6), (a, 7), respectively. Both Cartesian products are therefore not equal.


17) The Power set of the set A=,,,, has how many elements?

  1. 4 elements
  2. 6 elements
  3. 2 elements
  4. 5 elements

Answer: 4 elements

Explanation:

There are two components in Set Therefore, Set A's power set has four elements in total.


18) How many different sorts of mathematics are there?

  1. Mostly 2 types
  2. Mostly 3 types
  3. Mostly 5 types
  4. Mostly 4 types

Answer: 2 types

Explanation:

Discrete mathematics and continuous mathematics are the two subcategories of mathematics.


19) Which of the following functions is not a function used in mathematics?

  1. one-to-many
  2. many to one
  3. one to one
  4. All of the mentioned

Answer: one-to-many

Explanation:

None


20) Which of the following functions is not included in the definition of an "injective function"?

  1. One-to-One
  2. Many-to-one
  3. Onto
  4. None of the mentioned

Answer: One-to-One.

Explanation:

A function that relates a single element of a domain to a single element of a co-domain is known as an injective function or a one-to-one function.


21) What number of injections are defined from set A to set B if set A has four components and set B has five?

  1. 120
  2. 24
  3. 64
  4. 144

Answer: 120

Explanation:

120 injections are specified from set A to set B if set A has four elements and set B has five elements. The following formula makes it simple to calculate the injections:

Set A to Set B injections are as follows: 5p4 5! / (5 - 4)! = 5 x 4 x 3 x 2 = 120


22) What is the function (gof), if f and g are onto functions?

  1. Into function
  2. one-to-one function
  3. onto function
  4. one-to-many function

Answer: onto

Explanation:

If both functions f and g are "Onto functions," then the function (gof) is also a "Onto function."


23) How many bytes are required for 2000 bits of data to be encoded?

  1. 8 bytes
  2. 5 Byte
  3. 2 bytes
  4. 4 bytes

Answer: 2 bytes

Explanation:

The 2000 bits of data can be encoded using just 2 bytes.


24) How many even positive integers are there that are less than twenty?

  1. 8
  2. 10
  3. 9
  4. 10

Answer: 9

Explanation:

The set of even positive integers under 20 has nine elements, which gives it a nine-member cardinality. The set contains the following nine elements: 2, 4, 6, 8, 10, 12, 14, and 18.


25) If X and Y are equal to 2, 8, 12, 15, 16, and 8, 16, 15, 18, respectively, then X and Y's union is __________.

  1. {2, 8, 12, 15, 16}
  2. {8, 16, 15, 18, 9}
  3. { 8, 16, 15}
  4. {2, 8, 9, 12, 15, 16, 18}

Answer: {2, 8, 9, 12, 15, 16, 18}

Explanation:

Since they are shared by both sets X and Y, the elements 8, 16, and 15 should only be used once in each set. Thus, the correct union of X and Y is formed by the numbers 2, 8, 9, 12, 15, 16, and 18.


26) What does the Floor function do?

  1. It converts the real number to the biggest integer before it
  2. It converts the real number to the smallest integer before it.
  3. It converts the real number to the next-smallest integer.
  4. None of the aforementioned

Answer: It maps the real number to the greatest previous integer

Explanation:

The greatest integer that is not greater than x is obtained using the floor function (f(x)), which takes a real number (x) as input.


27. What is the purpose of Ceil?

  1. It converts the real number into the next-smallest integer.
  2. It converts the actual number to the biggest integer before it.
  3. It converts the real number to the smallest integer before it.
  4. All of the above are not

Answer: In other words, it converts the real number to the next-smallest integer.

Explanation:

A real number, x, is converted to the smallest integer that is not x's value using the floor function, or f(x).


28) What does Floor(8.4) + Ceiling(9.9) equal?

  1. 18
  2. 17
  3. 20
  4. 19

Answer: 18

Explanation:

Because Floor(8.4) is worth 8 and Ceil(9.9) is worth 10, the value of Floor(8.4) + Ceil(9.9) is 18. 8 plus 10 equals 18, so.


29) What is Floor(a+b) and Ceil(a+b)'s maximum value? if two positive numbers smaller than one, a and b, are present.

  1. Ceil(a+b) = 1 and Floor(a+b) = 0.
  2. Ceil(a+b) is 2 and Floor(a+b) is 1.
  3. Ceil(a+b) = 0 and Floor(a+b) = 1.
  4. Ceil(a+b) is 1 and Floor(a+b) is 2.

Answer: Floor(a+b) is 1 and Ceil(a+b) is 2.

Explanation:

The answer to the question is that a and b are both 1, meaning that the maximum values of Floor(a+b) and Ceil(a+b) are 1 and 2, respectively.


30) If set X and set Y have 7 and 8 elements, respectively, how many relations exist between them?

  1. 256
  2. 272
  3. 356
  4. 56

Answer: 256

Explanation:

There are 2mn relations between sets X and Y, where m denotes the set X elements and n denotes the set Y elements. So, 27 x 8 = 256.


31) On the set "0, 1, 2, 3," the relation "(0, 1), (1, 1), (1,3), (2,1), (2,2), (3,0)" has the following number of reflexive closures: ________.

  1. 26
  2. 36
  3. 8
  4. 6

Answer: 6

Explanation: No Justification


32) The relation R = "(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)" has several transitive closures where "1, 2, 3, 4, 5" is A.

  1. {(0,0), (4,4), (5,5), (1,1), (2,2), (3,3)}
  2. {(0,1), (1,2), (2,2), (3,4)}
  3. {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}
  4. {(0,1), (5,3), (5,4), (1,1), (2,2)}

Answer: {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}

Explanation:

None


33) Which assertion is untrue if X and Y are the two non-empty relations on the set S?

  1. If two variables, X and Y, are transitive, then so is their intersection.
  2. If two variables X and Y are reflexive, then their intersection must likewise be reflexive.
  3. If two variables, X and Y, are symmetric, then their union is not symmetric.
  4. If two things, X and Y, are transitive, then their union is not.

Answer: If X and Y are transitive, then the union of X and Y is not transitive.

Explanation: None


34. Which choice represents the negation of the bit "1001011" in question?

  1. 11011011
  2. 0110100
  3. 10110100
  4. 1100100

Answer: 0110100

Explanation:

The value of the bits opposite to the ones provided is their negation. If a bit has a value of 1, its negation value is 0. Additionally, if a bit's value is 0, its negation value is 1, and vice versBecause of this, "0110100" is the negation of "1001011".


35) What is X's (Ex-or) output if X's bits are 001101 and Y's bits are 100110?

  1. X (Ex-or) Y output is 101011
  2. X (Ex-or) Y outputs 0010101
  3. X (Ex-or) Y produces the output 1101010.
  4. 101000 is the output of X (Ex-or) Y.

Answer: The result of X (Ex-or) Y is 101011

Explanation:

The result of the Ex-or operation is 0 if the inputs are the same, otherwise, it is 1.

Because of this, the provided bits' output as a consequence is 101011.


36) How many values are covered by Boolean algebra?

  1. There are just four discrete values involved.
  2. There are just three discrete values involved.
  3. There are just five discrete values involved.
  4. There are just two discrete values involved.

Answer: It deals with only two discrete values.

Explanation:

The only discrete values that boolean algebra deals with are 0 and 1. 1 denotes truth, and 0 denotes falsehood.


37) Which of the following Boolean logic proofs establishes that X.X=X?

  1. Identity Law
  2. Double Complement Law
  3. Complement Law
  4. Idempotent Law

Answer: Idempotent Law.

Explanation:

Proofs of the idempotent law AND form OR form. X+X=X and X.X=X are proved.


38) Which of the following propositions, as shown by the symmetric matrix, is correct?

  1. A = AT
  2. A = -AT
  3. A symmetric matrix has One as the value of each diagonal element.
  4. A symmetric matrix has zero values for all of its diagonal elements.

Answer: A = AT

Explanation:

A square matrix is a symmetric matrix, as explaineAs a result, its transpose is equivalent to the symmetric matrix that is provided.


39) Which of the following matrices has many columns but only one row?

  1. Diagonal Matrix
  2. Row Matrix
  3. Column Matrix
  4. None of the mentioned

Answer: Row Matrix

Explanation:

A matrix with one row and several columns is referred to as a row matrix. N is the number of columns in a row matrix, and 1 x N is the order of the row matrix.

The numerous row matrix examples are as follows:

1. [ 6 5 4 ]: This matrix's dimensions are 1 x 3, or one row by three columns.

2. [0]: This matrix's dimensions are 1 x 1, or 1 row and 1 column.

3. [1 2 0 6 8 9]: This matrix's dimensions are 1 x 6, or 1 row and 6 columns.


40) Which matrix out of the following contains many rows but only one column?

  1. A Diagonal Matrix
  2. A Row Matrix
  3. A Column Matrix
  4. None of the mentioned above.

Answer: Column Matrix.

Explanation:

A matrix with several rows and just one column is called a column matrix. N rows make up a column matrix, and 1 designates the row matrix's order.


41) Which of the following statements about adding two matrices is true?

  1. The two matrices we wish to add have identical rows and columns.
  2. The two matrices' columns that we want to add are equal. The rows of both matrices we want to add are identical.
  3. a The number of rows in the first matrix must match the number of columns we wish to add in the second matrix.
  4. The rows and columns of the two matrices we want to add are identical.

Answer: The two matrices we wish to add have identical rows and columns.

Explanation:

If we want to add the two matrices, their rows and columns are in the same order.


42) If the ordering of A and B matrices is the same, the assertion "A+B = B+A" is true or false.

  1. False
  2. True

Answer: True

Explanation:

Because the addition of two matrices is commutative, the assertion that A+B = B+A is true.


43) If the order of the A matrix and the B matrix is the same, the assertion "XY = YX" is either true or false.

  1. False
  2. True

Answer: False

Explanation:

Because the multiplication of two matrices is not commutative, the assertion XY = YX is false.


44) I am a universal logic gate.

  1. OR
  2. NOT
  3. AND
  4. NAND

Answer: NAND

Explanation:

The NAND logic gate may simply build or create all the other logic gates on its own, without the aid of the three fundamental logic gates.


45) In what year was the Karnaugh map first published by Maurice Karnaughin?

  1. 1952
  2. 1956
  3. 1953
  4. 1958

Answer: 1953

Explanation:

Maurice Karnaughin produced the Karnaugh map in 1953.


46) There are several types of canonical forms for boolean expressions.

  1. Mostly Two types
  2. Mostly Four types
  3. Mostly Three types
  4. Mostly Five types

Answer: Mostly Two types.

Explanation:

Canonical There are two forms of form for boolean expressions. One form is the sum of min-terms, whereas the first form is the product of max-terms.


47) ____________ uses boolean algebra

  1. in the development of algebraic functions.
  2. in the creation of logic symbols.
  3. in the development of digital computers.
  4. in circuit theory.

Answer: in designing digital computers.

Explanation:

The design of various electronic circuits and digital computers is where Boolean algebra is most frequently used.


48) How many values are covered by Boolean algebra?

  1. There are just four discrete values involved.
  2. There are just three discrete values involved.
  3. There are just five discrete values involved.
  4. There are just two discrete values involved.

Answer: There are only two discrete values involved.

Explanation:

The only discrete values that boolean algebra deals with are 0 and 1. 0 denotes false, whereas 1 denotes true.


49) Which search compares every element to the one being sought after until nothing is found?

  1. Merge search
  2. none of the mentioned
  3. Sequential Search
  4. Binary search

Answer: Sequential search

Explanation:

The search element is compared to each element of the given list individually using a sequential or linear search method until the search element cannot be found.


50) To sort a list of n unsorted entries, which element in the list initiates the insertion sort?

  1. The first element of the list
  2. the second element of the list
  3. the Third element of the given list
  4. the Fourth element of the given list

Answer: the second element of the list

Explanation:

If a user wishes to use the insertion sort to order the unsorted list of n elements. The second element of the list is when the sorting algorithm begins sorting.


51) What is the complexity of the bubble sort algorithm?

  1. O(n)
  2. O(log n),
  3. O(n log n),
  4. O(n2)

Answer: O(n2)

Explanation:

The complexity of the bubble sort algorithm is O(n2), where n is the number of sorted entries in the list.


52) What is a linear search algorithm's worst-case scenario?

  1. When the item you are looking for appears in the midst of the list.
  2. When the search results aren't in the list.
  3. When the item you are looking for is the last one on the list.
  4. When the item you are seeking for is the last one on the list or not at all.

Answer: When the search item is either the last item on the list or not there at all.

Explanation:

When the object being looked for is the very last item in the list or not at all, a linear search algorithm performs worst-case scenarios.


53) Which algorithm finds the new outputs using the prior outputs?

  1. Divide and Conquer algorithm
  2. Dynamic Programming algorithms
  3. Brute Force algorithm
  4. None of them

Answer: Dynamic Programming algorithms

Explanation:

Algorithms for dynamic programming are those that generate new outputs based on prior results from the same problem.


54) Which choice represents an algorithm in the right way?

  1. Flow charts
  2. Pseudo codes
  3. Statements in the common language
  4. All of them

Answer: All of them

Explanation:

For describing the algorithm, pseudocodes, flowcharts, and a statement in everyday language are all employed.


55) Which scenario does complexity theory not consider?

  1. Average case
  2. Best case
  3. Null case
  4. Worst Case

Answer: Null case

Explanation:

In the complexity theory, the three situations of average, worst, and best are always possible. In the theory of complexity, there is no Null case.


56. A field of mathematics that uses discrete elements is known as discrete mathematics.

  1. algebra
  2. arithmetic
  3. Both A and B
  4. None of the above

Answer: C

Explanation:

When dealing with discrete elements, discrete mathematics, a subfield of mathematics, uses algebra and arithmetic.


57. Discrete items are distinct from (not related to) and isolated from one another.

  1. TRUE
  2. FLASE
  3. MAYBE
  4. CAN'T SAY

Answer: TRUE

Explanation:

Discrete items are distinct from (not related to) and isolated from one another.


58. In which of the following situations can discrete objects be considered?

  1. people
  2. Integers
  3. Rational numbers
  4. All of the above

Answer :

All of the above

Explanation:

Automobiles, homes, people, and other discrete objects are all examples of integers (also known as whole numbers), rational numbers (numbers that can be written as the quotient of two integers), and so on.


59. Real numbers, which can be both rational and irrational, are not discrete.

  1. Real numbers which include irrational are discrete
  2. FALSE
  3. rational numbers are discrete
  4. TRUE

Answer: TRUE

Explanation:

Real numbers are not discrete, and this includes both rational and irrational numbers.


60. How many broad categories can mathematics be placed under?

  1. 2
  2. 3
  3. 4
  4. 5

Answer: 2

Explanation:

Discrete mathematics and continuous mathematics are the two broad categories into which mathematics may be divided.


61. Which of the following has separate values, that is, values between any two points?

  1. Non-Discrete Mathematics
  2. Continuous Mathematics
  3. Non-Continuous Mathematics
  4. Discrete Mathematics

Answer: Discrete Mathematics

Explanation:

In discrete mathematics, distinct values are employed, which means that there are discrete numbers of points separating any two points.


62. Which of the following statement is a proposition?

  1. Get me a glass of milkshake
  2. God bless you!
  3. What is the time now?
  4. The only odd prime number is 2

Answer: The only odd prime number is 2

Explanation:

Only this assertion is false and has the truth value.


63. Which of the following option is true?

  1. 3 +2 = 8 if 5-2 = 7
  2. 1 3 and 3 is a positive integer
  3. -2 3 or 3 is a negative integer
  4. If the Sun is a planet, elephants will fly

Answer: 3+2=8 if 5-2=7

Explanation:

The entire sentence is true because the hypothesis is untrue.


64. What bit is the opposite of "010110" in the following list?

  1. 111001
  2. 101101
  3. 101001
  4. 111111

Answer: 101001

Explanation:

To obtain the negative of the necessary string, flip each bit.


65. How many bits of the string of length 4 are possible such that they contain 2 ones and 2 zeroes?

  1. 7
  2. 5
  3. 6
  4. 4

Answer: 6

Explanation:

The strings are {0011, 0110, 1001, 1100, 1010 and 0101}.


66. Who introduced the concept of sets?

  1. Babylonians
  2. Konrad Zuse
  3. Pythagoreans
  4. G. Cantor

Answer: G. Cantor

Explanation:

The idea of sets was first presented by German mathematician G. Cantor.


67. Several additional branches of research, such as?, are founded on set theory.

  1. counting theory
  2. relations
  3. finite state machines
  4. All of the above

Answer: All of the above

Explanation:

Numerous other academic disciplines, including counting theory, relations, graph theory, and finite state machines, are built on the foundation of set theory.


68. The term "set" refers to a grouping of various elements.

  1. an unordered set
  2. an ordered set
  3. unordered set and ordered set
  4. None of the above

Answer: an unordered set

Explanation:

An unsorted collection of several items is referred to as a set.


69. A set can be written explicitly by listing its elements using?

  1. ()
  2. []
  3. {}
  4. " "

Answer: {}

Explanation:

The elements of a set can be listed explicitly by using set brackets.


70. How many different ways are there to express sets?

  1. 2
  2. 3
  3. 4
  4. 5

Answer: 2

Explanation:

There are two ways to express sets: in roster or tabular form, and in set builder notation.


71. A={a,e, i,o,u} is an example of a?

  1. Set Builder Notation
  2. Roster Form
  3. Both A and B
  4. None of the above

Answer: Roster form

Explanation:

It is an illustration of a tabular or roster form.


72. What does Z+ stand for in 72?

  1. The collection of all rational numbers
  2. the collection of all positive numbers
  3. the collection of every whole number
  4. the collection of all real numbers

Answer: The collection of all rational numbers

Explanation:

The collection of all positive integers, or Z+, is explained.


73. A set that contains a definite number of elements is called?

  1. a Proper Subset
  2. a Universal Set
  3. A Finite Set
  4. a Unit Set

Answer: Finite Set

Explanation:

A finite set has exactly that many elements.


74. Which of the following provides a count of the various ways a set can be divided?

  1. Bell Numbers
  2. Cross Numbers
  3. Complement Numbers
  4. Power Numbers

Answer: Bell Numbers

Explanation:

Which of the following gives the total number of possible methods to divide a set?


75. The power set of an empty set is?

  1. 0
  2. 1
  3. 2
  4. empty set

Answer: the empty set

Explanation:

An empty set also exists as the power set of an empty set.


76. Relations may exist between?

  1. objects of the same set
  2. between objects of two or more sets.
  3. Both A and B together
  4. None of the above

Answer: Both A and B

Explanation:

Relations could occur between things belonging to the same set or between objects belonging to two or more sets.


77. single set and the binary relation R A is a part of what?

  1. A X A
  2. A % A
  3. A ^ A
  4. A ? A

Answer: A X A

Explanation:

binary relationship R on just one set A is part of the set AA.


78. The maximum cardinality of a relation R from two distinct sets A and B with respective cardinalities m and n is?

  1. m+n,
  2. m*n,
  3. mn,
  4. Aside from that,

Answer: m*n

Explanation:

A relation R from two distinct sets A and B with respective cardinalities of m and n has a maximum cardinality of mn.


79. A can be used to represent a relation.

  1. Undirected graph
  2. Pie graph
  3. Directed graph
  4. Line graph

Answer: Directed graph

Explanation:

A directed graph can be used to depict a relation.


80. Set XY is the set XY Relation between sets X and Y.

  1. an Empty set
  2. a Full set
  3. an Identity set
  4. an Inverse set

Answer: Full

Explanation:

Set XY is the full relationship between sets X and Y.


81. If xRy entails yRx, a relation R on set A is said to be _________.

  1. Reflexive in nature
  2. Irreflexive in nature
  3. Anti-Symmetric in nature
  4. Symmetric in nature

Answer: Symmetric

Explanation:

If xRy implies yRx, a relation R on set A is said to be symmetric in nature.


82. On the set X="a,b," what is the relation R="(a,b),(b,a)"?

  1. Irreflexive
  2. Anti-Symmetric
  3. Reflexive
  4. Symmetric

Answer: Irreflexive

Explanation:

On the set X=a,b, the relation R=(a,b),(b,a) is irreflexive.


83. The relation R=(a,b),(b,a) is irreflexive on the set X=a,b.

  1. transitive rather than reflective, irreflexive, or both
  2. transitive, symmetric, and irreflexive
  3. Transitive, symmetrical, and reflecting
  4. antisymmetrical and irreflexive

Answer: transitive, not reflective, not irreflexive.

Explanation:

Not symmetric since (2, 1) but not (1, 2) are present; not antisymmetric because (2, 3) and (3, 2) are present; not asymmetric because asymmetry needs both antisymmetry and reflexivity. Not irreflexive = not present (3, 3); not reflexive = present (1, 1). The relationship is thus transitively closed.


84. A = (a,b) | b = a - 1 is a binary relation, and a and b are members of the set 1, 2, and 3. What is A's reflexive transitive closure?

  1. {(a,b) | a = b and a, b belong to {1, 2, 3}}
  2. {(a,b) | a b and a, b belong to {1, 2, 3}}
  3. {(a,b) | a = b and a, b belong to {1, 2, 3}}
  4. {(a,b) | a <= b and a, b belong to {1, 2, 3}}

Answer: {(a,b) | a = b and a, b belong to {1, 2, 3}}

Explanation:

According to the concept of transitive closure, and is linked to every smaller b (since every an is related to b - 1)), and an is related to a based on the reflexive property.


85. The computation of the transitive closure of a binary relation on a set of n elements should take ________ seconds.

  1. O(login)
  2. O(n)
  3. O(n^3)
  4. O(n^2)

Answer: O(n^3)

Explanation:

Matrix multiplication is the outcome of the transitive closure calculation. Matrix multiplication can be completed in O(n3) time. Better algorithms exist that perform in less time than cubic time.


86. Functions or mappings (f:X-Y) are used to describe relationships between the elements of two sets, such as those between X and Y.

  1. Codomain
  2. image of the function
  3. Domain
  4. pre-image

Answer: Domain

Explanation:

It is known as a function or mapping (define as f:X-Y) when there is a relationship between items of one set X and elements of another set Y (X and Y are non-empty sets). The domain is the name of X.


87. Can't a function be?

  1. one too many functions.
  2. many-to-one function
  3. one-to-one function
  4. All of the above

Answer: one too many functions

Explanation:

One-to-one or many-to-one functions are both acceptable but not one-to-many.


88. is f:N-N, f(x)=5x?

  1. not injective
  2. injective
  3. surjective
  4. inverse

Answer: injective

Explanation:

F(x)=5x is injective with f: N-


89. A function is defined as ___________ (onto) if its image equals its range.

  1. injective
  2. Not surjective
  3. inverse
  4. surjective

Answer: surjective

Explanation:

If the image of a function f: A-B equals its range, the function is surjective (onto).


90. What is known as if a function is both surjective and injective?

  1. a bijective
  2. a composition
  3. a invertible
  4. a associative

Answer: a bijective

Explanation:

F is bijective because it has both surjective and injective properties.


91. The function (gof), if f and g are on, is?

  1. one to one
  2. into
  3. one too many.
  4. onto

Answer: onto

Explanation:

The function (gof) is also onto if f and g are.


92. Which of these the Composition does not hold?

  1. an associative property
  2. a commutative property
  3. a one-to-one function
  4. Both A and B may be

Answer: a commutative property.

Explanation:

Composition does not have commutative property, but it always has associative property.


93. Let f and g stand in for the function from the set of integers to itself if, respectively, f(x) and g(x) are 2x + 1 and 3x + 4, respectively. Following that, f and g are composed of __________.

  1. 6x+8
  2. 6x+3
  3. 6x+7
  4. 6x+9

Answer: 6x+9

Explanation:

The formula f(g(x)) yields the composition of f and g as 2(3x + 4) + 1


94. 2000 bits of data need to be encoded in __________ bytes.

  1. 4
  2. 2
  3. 8
  4. 1

Answer: 2

Explanation:

2000 can be encoded using two bytes, however, two bytes can also encode values up to and including 65,535.


95. Which of the following is true?

  1. From R to R, the function f(x) = x3 is a bijection.
  2. From the set of integers to itself, the function f(x)=x+1 is onto.
  3. A and B both
  4. None of the preceding

Answer: The same as A and B.

Explanation:

The proverb "A and B are true" is true, as explained.


97. Who developed the earliest technique for manipulating symbolic logic?

  1. Babylonians
  2. Konrad Zuse
  3. George Boole
  4. G. Cantor

Answer: George Boole

Explanation:

The first method of handling symbolic logic was developed by George Boole and is now referred to as Boolean algebra.


98. What Boolean Identities demonstrate that A+A=A?

  1. an Idempotent Law
  2. a Double Complement Law
  3. a Complement Law
  4. an Identity Law

Answer: Idempotent Law

Explanation:

A+A=A (OR Form) and A.A=A (AND Form) are examples of idempotent law.


99. Which of the Boolean Identities law proof as given A+1=1?

  1. a Commutative Law
  2. an Absorption Law
  3. an Associative Law
  4. a Dominance Law

Answer: Dominance Law

Explanation:

Rule of Dominance: A.0=0 (AND Form) and A.+1=1 (OR Form)


100. All variables, whether in their direct or supplemented form, result in a _____________.

  1. minterm
  2. mixterm
  3. variables
  4. None of the above

Answer: minterm

Explanation:

Each variable, whether it is taken directly or complementarily, results in a minterm, which is the sum of all the minterms. Any Boolean function may be written as the product of its 1-minterms, and its inverse can be written as the product of its 0-minterms.


101. The Karnaugh map (K-map), first introduced by Maurice Karnaugh, was first used in?

  1. 1952
  2. 1950
  3. 1953
  4. 1956

Answer: 1953

Explanation:

Maurice Karnaughin introduced the Karnaugh map (K-map) first 1953.


102. The logic gate that produces high output for identical inputs but low output otherwise is known as?

  1. NOT
  2. XOR
  3. AND
  4. X-NOR

Answer: X-NOR

Explanation:

The X-NOR or Exclusive NOR gate is a type of logic gate that produces high output for identical inputs but low output otherwise.


103. How many different Boolean expression canonical forms are there?

  1. 5
  2. 2
  3. 3
  4. 4

Answer: 2

Explanation:

A Boolean expression can take one of two canonical forms: either the sum of the terms (SOM) form or the product of the terms (SOM)


104. F(X, Y, Z, and M) = X'Y'Z'M'. The function's degree is ________.

  1. 5
  2. 3
  3. 2
  4. 4

Answer: 4

Explanation:

This is a function of degree 4 that transfers the set of ordered pairs of Boolean variables to the set "0, 1".


106. A collection of points is known as a graph.

  1. Edge
  2. Nodes
  3. fields
  4. lines

Answer: Nodes

Explanation:

A graph is made up of a collection of nodes or vertices connected by a collection of edges.


107. The graph is made up of a?

  1. a non-empty set of vertices
  2. an empty set of vertices
  3. Both A and B
  4. None of the above

Answer: a non-empty set of vertices

Explanation:

A graph is made up of a set of edges (E) and a set of non-empty vertices (V).


108. What is the term for the number of edges that the vertex V has?

  1. Degree of a vertex
  2. Handshaking Lemma
  3. Degree of a Graph
  4. None of the above

Answer: Degree of a Vertex

Explanation:

Degree of a Vertex The number of edges that intersect a vertex V in a graph G (designated by the symbol deg (V)) determines its degree.


109. In reference to the Handshaking Lemma, which of the following claims is true?

  1. According to the Handshaking lemma, a vertex is referred to as an even vertex if its degree is even.
  2. The number of edges is equal to twice the sum of all the vertices' degrees.
  3. When a vertex's degree is odd, it is referred to as an odd vertex.
  4. A graph's degree is equal to its highest vertex degree.

Answer: The number of edges is equal to twice the sum of all the vertices' degrees.

Explanation:

The Handshaking Lemma explains that in a graph, the sum of the degrees at each vertex is equal to twice the sum of the edges.


110. Explain the Null Graph.

  1. No nodes exist in a null graph.
  2. No even or odd vertex exists in the null graph

No edges exist in the null graph

Answer: The null graph has no edges, so

Explanation:

There are no edges in a null graph.


111. In a graph, what is it called when numerous edges are permitted between the same set of vertices?

  1. Multi graph
  2. Simple graph
  3. Hamiltonian Graphs
  4. Euler Graphs

Answer: Multi graph

Explanation: A graph is referred to as a multigraph if numerous edges between the same set of vertices are permitted.


112. What is the name of the graph where every edge of the graph is covered by a closed trail?

  1. Hamiltonian Graphs
  2. Directed Graph
  3. Planar graph
  4. Euler Graphs

Answer: Euler Graphs

Explanation:

If there is a closed trail that spans every edge of the connected graph, it is referred to as an Euler graph.


113. A directed cyclic network with nodes at 7 should have an equal number of Hamiltonian cycles.

  1. 540
  2. 720
  3. 360
  4. 180

Answer: 360

Explanation: a connected graph with a Hamiltonian cycle G is defined as a closed path that passes through each vertex exactly once, with the exception of the initial vertex, where the path also ends. An n-complete graph contains (n-1)!/2 Hamiltonian cycles, hence the answer is 360.


114. If G is a forest of 54 vertices and 17 connected components, then G has a total of _______ edges.

  1. 35
  2. 36
  3. 37
  4. 38

Answer: 37

Explanation:

Here, a forest with 54 vertices and 17 components is presented to us. Since a component is a tree in and of itself, the fact that there are 17 components implies that each component has a root, giving us a total of 17 roots. A single edge of a forest is created by each new vertex in the woodlanThe remaining 54-17 = 37 vertices can therefore have m-n=37 edges. Thus, the solution is 37.


115. Triangle-free graphs possess the characteristic that their clique number is _____.

  1. greater than 3
  2. less than 5
  3. equal to 5
  4. More than 10

Answer: more than 10

Explanation:

No triangle of edges may be formed by three vertices in an undirected triangle-free graph. It can be categorized as graphs having a girth of more than four and a clique number of less than two.


116. How is a tree connected?

  1. acyclic undirected graph
  2. cyclic undirected graph
  3. acyclic directed graph
  4. cyclic directed graph

Answer: acyclic undirected graph

Explanation:

A connected acyclic undirected graph is a tree.


117. What does a tree with N vertices contain?

  1. (N+1) Edges
  2. (N^2)-1 Edges
  3. N Edges
  4. (N-1) Edges

Answer: (N-1) Edges

Explanation:

(N1) A number of edges make up a tree with N number of vertices.


118. What is the name of the vertex with a degree of 0?

  1. Root
  2. Leaf
  3. Internal node
  4. None of the above

Answer: root

Explanation:

The root of the tree is the vertex with a degree of zero. The leaf node of the tree is the vertex with a degree of 1, while an internal node has a degree of at least 2.


119. A ___________ tree is a tree whose vertices are each given a distinct number between 1 and n.

  1. Centers
  2. Bi- Centers
  3. Unlabeled
  4. labeled

Answer: labeled

Explanation:

A labeled tree is a tree whose vertices are each given a distinct number between 1 and n.


120. how many edges are considered to have an incident with the vertex V?

  1. O(log n)
  2. O(n)
  3. O(n^2)
  4. O(nlog n)

Answer: O(n)

Explanation:

The average complexity for insertion is O(log n), and the worst case is O(n).


121. What exactly is a binary search tree's space complexity?

  1. O(logn)
  2. O( n)
  3. O(n^2)
  4. O(nlog n)

Answer: O(n)

Explanation:

Space complexity: O(n) in the worst case and O(n) in average complexity.

  1. 122. How many k numbers of vertices labeled trees are there?
  2. k^(n-2)
  3. k^(n-1)
  4. k^(n)
  5. k^(2)

Answer: k^(n-2)

Explanation:

The number of labeled trees with k vertices is equal to k(n-2).


123. Vertices in a linear graph are arranged in a line.

  1. TRUE
  2. FLASE
  3. either true or false
  4. cannot be determined

Answer: FALSE

Explanation:

A linear graph, commonly referred to as a path graph, is a graph with k vertices organized in a line such that edges connecting vertices from I and i+1 for i=0,..., k-1.


124. What about star tree is accurate?

  1. A tree with n leaves and a single internal vertex
  2. A tree with n vertices and n-1 cycles is option B.
  3. A tree with n vertices in a straight line.
  4. A tree with 0 or more connected subtrees

Answer: a tree with n leaves and a single internal vertex

Explanation:

In other words, a star tree is a tree with n leaves and a single internal vertex. A tree with all of its potential leaves is known as a star tree of order n. But a vertex with at least a degree of two is considered an internal vertex.


125. If a tree just possesses one quirk, it is referred to as

  1. Bi-Centers
  2. Central Tree
  3. Rooted Tree
  4. Labeled Trees

Answer: Central Tree

Explanation:

Bi-central trees are those that only have two or more centers.


126. When was probability theory created?

  1. 1638
  2. 1674
  3. 1654
  4. 1666

Answer: 1654

Explanation:

The first research into probability was conducted by Gerolamo Cardano in the 1560s (although they were not published until 100 years later), and the second was the correspondence between Pierre de Fermat and Blaise Pascal in 1654.


127. When we experiment, the set S of all potential results is referred to as the?

  1. Sample Space
  2. Event
  3. Random Experiment
  4. Tossing Space

Answer: Sample Space

Explanation:

Sample Room The sample space is the set S of all potential outcomes when we experiment.


128. How many alternative outcomes are there when a coin is tossed?

  1. 4
  2. 1
  3. 3
  4. 2

Answer: 2

Explanation:

When a coin is tossed, one of two possible results is possible: heads or tails.


129. What is the likelihood that any particular number will appear on a roll of the dice?

  1. (1/6)
  2. (5/6)
  3. (2/3)
  4. (1/3)

Answer: (1/6)

Explanation:

Any one of the numbers has a 1/6 probability


130. Find the likelihood of drawing an ace if one card is chosen at random from a deck of 52 cards.

  1. (1/52)
  2. (1/13)
  3. (3/52)
  4. (1/26)

Answer: (1/13)

Explanation:

Find the likelihood of drawing an ace if one card is chosen at random from a deck of 52 cards...


131. Find the likelihood that a diamond will be drawn if one card is chosen at random from a deck of 52 cards.

  1. (1/6)
  2. (3/26)
  3. (1/13)
  4. (1/4)

Answer: (1/4)

Explanation:

13/52, or one-fourth, of something being a diamond.


132. Discrete probability distribution is dependent on ___________'s characteristics.

  1. discrete variables
  2. probability function
  3. data
  4. machine

Answer: data

Explanation:

We are aware that discrete probability functions heavily rely on the characteristics and types of data, such as how binary data, like coin flipping, can be modeled by the binomial distribution.


133. A bag contains a few blue balls and five red balls. If there are twice as many blue balls in a bag as there are red balls, then the probability of drawing a blue ball is:

  1. 10
  2. 20
  3. 5
  4. 15

Answer: 10

Explanation:

If there are x blue balls, then there will be a total of 5 + x balls. The answer is that x/(5 + x) = 2 and X (5/5+x) x = 10.


134. Cards with numbers 2 through 101 are put in a box and properly mixeThe likelihood that the card's number is a perfect square is determined when one card is picked at random from this box.

  1. (1/5)
  2. (1/25)
  3. (1/10)
  4. (1/20)

Answer: (1/10)

Explanation:

The integers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are all perfect squares between 2 and 101. Totals from 2 to 101 equal 100. The odds of drawing a card with a perfect square number are as follows: P (perfect square) = 10/100 P (perfect square) = 1/10.


135. The mean annual wages of employees at a sizable manufacturing facility are Rs. 48,000, and the standard deviation is Rs. 1500. Calculate the likelihood that a worker makes between Rs. 35,000 and Rs. 52,000.

  1. 0.42
  2. 0.423
  3. 0.421
  4. 0.422

Answer: 0.421

Explanation:

Z is equal to -2 for x = 45000 and 0.375 for x = 52000. Now, 42.1% of people who live in the region between z = -2 and z = 0.375 earn between Rs. 45,000 and Rs. 52,000.






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