## Discrete Mathematics Functions Questions And Answers
- The Set is a Finite Set.
- The set is an Empty set
- The set is a Non-empty set
- The Set is both Non- empty set and a Finite set.
Set 0 is the non-empty, finite set.
- Infinite set
- Not a set
- Finite set
- Empty set
Since there is no extreme prime, there are an endless amount of primes.
- Empty set
- Finite set
- Infinite set
- None of the mentioned
Infinite real numbers between 1 and 2 make up the infinite set X.
- {1, 2}
- {1, 2, 3}
- {1}
- All of the mentioned
- {∅}
- {3, 5, 7}
- {2, 3}
- {2, 3, 7}
Two and three are the prime divisors of 72. The roster form for set x is therefore (2, 3).
- Two
- One
- Zero
- Three
- { (1, a), (1, b), (2, a), (b, b) }
- { (1, 1), (a, a), (2, a), (1, b) }
- { (1, 1), (2, 2), (a, a), (b, b) }
- { (1, a), (2, a), (1, b), (2, b) }
A subset R of the Cartesian product A x B is a relation from set A to set B.
- {0, 2, 4, 5, 9, 55, 46, 49, 99, 81}
- {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
- {1, 4, 9, 16}
- {0, 1, 4, 9, 25, 36, 49, 123}
The set S contains the square of any number less than 10. The third option is therefore the best one given the alternatives.
- {5, 6, 12, 15}
- {1, 2, 10}
- {2, 5, 10, 9}
- {1, 6, 12, 9, 8}
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.
- {3, 8}
- {1, 3}
- {5, 6, 8}
- {2, 6, 5}
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).
- 30
- 20
- 40
- 10
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.
- 16
- 4
- 8
- 10
None
- Integers
- People
- Rational numbers
- All of the mentioned
People, homes, integers, rational numbers, and cars are examples of discrete objects.
- X = {5, 6} and Y = {6}
- X = {5, 6, 9} and Y = {5, 6}
- X = {5, 6, 8, 9} and Y = {6, 8, 5, 9}
- X = {5, 6} and Y = {5, 6, 3}
Given that the elements in both X and Y sets are the same, the second possibility is correct.
- 8
- 5
- 6
- 10
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.
- Yes
- No
- None of the above
- I don't know
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.
- 4 elements
- 6 elements
- 2 elements
- 5 elements
There are two components in Set Therefore, Set A's power set has four elements in total.
- Mostly 2 types
- Mostly 3 types
- Mostly 5 types
- Mostly 4 types
Discrete mathematics and continuous mathematics are the two subcategories of mathematics.
- one-to-many
- many to one
- one to one
- All of the mentioned
None
- One-to-One
- Many-to-one
- Onto
- None of the mentioned
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.
- 120
- 24
- 64
- 144
Set A to Set B injections are as follows: 5p4 5! / (5 - 4)! = 5 x 4 x 3 x 2 = 120
- Into function
- one-to-one function
- onto function
- one-to-many function
If both functions f and g are "Onto functions," then the function (gof) is also a "Onto function."
- 8 bytes
- 5 Byte
- 2 bytes
- 4 bytes
The 2000 bits of data can be encoded using just 2 bytes.
- 8
- 10
- 9
- 10
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.
- {2, 8, 12, 15, 16}
- {8, 16, 15, 18, 9}
- { 8, 16, 15}
- {2, 8, 9, 12, 15, 16, 18}
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.
- It converts the real number to the biggest integer before it
- It converts the real number to the smallest integer before it.
- It converts the real number to the next-smallest integer.
- None of the aforementioned
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.
- It converts the real number into the next-smallest integer.
- It converts the actual number to the biggest integer before it.
- It converts the real number to the smallest integer before it.
- All of the above are not
A real number, x, is converted to the smallest integer that is not x's value using the floor function, or f(x).
- 18
- 17
- 20
- 19
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.
- Ceil(a+b) = 1 and Floor(a+b) = 0.
- Ceil(a+b) is 2 and Floor(a+b) is 1.
- Ceil(a+b) = 0 and Floor(a+b) = 1.
- Ceil(a+b) is 1 and Floor(a+b) is 2.
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.
- 2
^{56} - 2
^{72} - 3
^{56} - 56
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.
- 26
- 36
- 8
- 6
- {(0,0), (4,4), (5,5), (1,1), (2,2), (3,3)}
- {(0,1), (1,2), (2,2), (3,4)}
- {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)}
- {(0,1), (5,3), (5,4), (1,1), (2,2)}
None
- If two variables, X and Y, are transitive, then so is their intersection.
- If two variables X and Y are reflexive, then their intersection must likewise be reflexive.
- If two variables, X and Y, are symmetric, then their union is not symmetric.
- If two things, X and Y, are transitive, then their union is not.
- 11011011
- 0110100
- 10110100
- 1100100
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".
- X (Ex-or) Y output is 101011
- X (Ex-or) Y outputs 0010101
- X (Ex-or) Y produces the output 1101010.
- 101000 is the output of X (Ex-or) Y.
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.
- There are just four discrete values involved.
- There are just three discrete values involved.
- There are just five discrete values involved.
- There are just two discrete values involved.
The only discrete values that boolean algebra deals with are 0 and 1. 1 denotes truth, and 0 denotes falsehood.
- Identity Law
- Double Complement Law
- Complement Law
- Idempotent Law
Proofs of the idempotent law AND form OR form. X+X=X and X.X=X are proved.
- A = AT
- A = -AT
- A symmetric matrix has One as the value of each diagonal element.
- A symmetric matrix has zero values for all of its diagonal elements.
A square matrix is a symmetric matrix, as explaineAs a result, its transpose is equivalent to the symmetric matrix that is provided.
- Diagonal Matrix
- Row Matrix
- Column Matrix
- None of the mentioned
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:
- A Diagonal Matrix
- A Row Matrix
- A Column Matrix
- None of the mentioned above.
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.
- The two matrices we wish to add have identical rows and columns.
- The two matrices' columns that we want to add are equal. The rows of both matrices we want to add are identical.
- a The number of rows in the first matrix must match the number of columns we wish to add in the second matrix.
- The rows and columns of the two matrices we want to add are identical.
If we want to add the two matrices, their rows and columns are in the same order.
- False
- True
Because the addition of two matrices is commutative, the assertion that A+B = B+A is true.
- False
- True
Because the multiplication of two matrices is not commutative, the assertion XY = YX is false.
- OR
- NOT
- AND
- NAND
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.
- 1952
- 1956
- 1953
- 1958
Maurice Karnaughin produced the Karnaugh map in 1953.
- Mostly Two types
- Mostly Four types
- Mostly Three types
- Mostly Five types
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.
- in the development of algebraic functions.
- in the creation of logic symbols.
- in the development of digital computers.
- in circuit theory.
The design of various electronic circuits and digital computers is where Boolean algebra is most frequently used.
- There are just four discrete values involved.
- There are just three discrete values involved.
- There are just five discrete values involved.
- There are just two discrete values involved.
The only discrete values that boolean algebra deals with are 0 and 1. 0 denotes false, whereas 1 denotes true.
- Merge search
- none of the mentioned
- Sequential Search
- Binary search
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.
- The first element of the list
- the second element of the list
- the Third element of the given list
- the Fourth element of the given list
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.
- O(n)
- O(log n),
- O(n log n),
- O(n2)
The complexity of the bubble sort algorithm is O(n2), where n is the number of sorted entries in the list.
- When the item you are looking for appears in the midst of the list.
- When the search results aren't in the list.
- When the item you are looking for is the last one on the list.
- When the item you are seeking for is the last one on the list or not at all.
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.
- Divide and Conquer algorithm
- Dynamic Programming algorithms
- Brute Force algorithm
- None of them
Algorithms for dynamic programming are those that generate new outputs based on prior results from the same problem.
- Flow charts
- Pseudo codes
- Statements in the common language
- All of them
For describing the algorithm, pseudocodes, flowcharts, and a statement in everyday language are all employed.
- Average case
- Best case
- Null case
- Worst Case
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.
- algebra
- arithmetic
- Both A and B
- None of the above
When dealing with discrete elements, discrete mathematics, a subfield of mathematics, uses algebra and arithmetic.
- TRUE
- FLASE
- MAYBE
- CAN'T SAY
Discrete items are distinct from (not related to) and isolated from one another.
- people
- Integers
- Rational numbers
- All of the above
All of the above
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.
- Real numbers which include irrational are discrete
- FALSE
- rational numbers are discrete
- TRUE
Real numbers are not discrete, and this includes both rational and irrational numbers.
- 2
- 3
- 4
- 5
Discrete mathematics and continuous mathematics are the two broad categories into which mathematics may be divided.
- Non-Discrete Mathematics
- Continuous Mathematics
- Non-Continuous Mathematics
- Discrete Mathematics
In discrete mathematics, distinct values are employed, which means that there are discrete numbers of points separating any two points.
- Get me a glass of milkshake
- God bless you!
- What is the time now?
- The only odd prime number is 2
Only this assertion is false and has the truth value.
- 3 +2 = 8 if 5-2 = 7
- 1 3 and 3 is a positive integer
- -2 3 or 3 is a negative integer
- If the Sun is a planet, elephants will fly
The entire sentence is true because the hypothesis is untrue.
- 111001
- 101101
- 101001
- 111111
To obtain the negative of the necessary string, flip each bit.
- 7
- 5
- 6
- 4
The strings are {0011, 0110, 1001, 1100, 1010 and 0101}.
- Babylonians
- Konrad Zuse
- Pythagoreans
- G. Cantor
The idea of sets was first presented by German mathematician G. Cantor.
- counting theory
- relations
- finite state machines
- All of the above
Numerous other academic disciplines, including counting theory, relations, graph theory, and finite state machines, are built on the foundation of set theory.
- an unordered set
- an ordered set
- unordered set and ordered set
- None of the above
An unsorted collection of several items is referred to as a set.
- ()
- []
- {}
- " "
The elements of a set can be listed explicitly by using set brackets.
- 2
- 3
- 4
- 5
There are two ways to express sets: in roster or tabular form, and in set builder notation.
- Set Builder Notation
- Roster Form
- Both A and B
- None of the above
It is an illustration of a tabular or roster form.
- The collection of all rational numbers
- the collection of all positive numbers
- the collection of every whole number
- the collection of all real numbers
The collection of all positive integers, or Z+, is explained.
- a Proper Subset
- a Universal Set
- A Finite Set
- a Unit Set
A finite set has exactly that many elements.
- Bell Numbers
- Cross Numbers
- Complement Numbers
- Power Numbers
Which of the following gives the total number of possible methods to divide a set?
- 0
- 1
- 2
- empty set
An empty set also exists as the power set of an empty set.
- objects of the same set
- between objects of two or more sets.
- Both A and B together
- None of the above
Relations could occur between things belonging to the same set or between objects belonging to two or more sets.
- A X A
- A % A
- A ^ A
- A ? A
binary relationship R on just one set A is part of the set AA.
- m+n,
- m*n,
- mn,
- Aside from that,
A relation R from two distinct sets A and B with respective cardinalities of m and n has a maximum cardinality of mn.
- Undirected graph
- Pie graph
- Directed graph
- Line graph
A directed graph can be used to depict a relation.
- an Empty set
- a Full set
- an Identity set
- an Inverse set
Set XY is the full relationship between sets X and Y.
- Reflexive in nature
- Irreflexive in nature
- Anti-Symmetric in nature
- Symmetric in nature
If xRy implies yRx, a relation R on set A is said to be symmetric in nature.
- Irreflexive
- Anti-Symmetric
- Reflexive
- Symmetric
On the set X=a,b, the relation R=(a,b),(b,a) is irreflexive.
- transitive rather than reflective, irreflexive, or both
- transitive, symmetric, and irreflexive
- Transitive, symmetrical, and reflecting
- antisymmetrical and irreflexive
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.
- {(a,b) | a = b and a, b belong to {1, 2, 3}}
- {(a,b) | a b and a, b belong to {1, 2, 3}}
- {(a,b) | a = b and a, b belong to {1, 2, 3}}
- {(a,b) | a <= b and a, b belong to {1, 2, 3}}
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.
- O(login)
- O(n)
- O(n^3)
- O(n^2)
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.
- Codomain
- image of the function
- Domain
- pre-image
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.
- one too many functions.
- many-to-one function
- one-to-one function
- All of the above
One-to-one or many-to-one functions are both acceptable but not one-to-many.
- not injective
- injective
- surjective
- inverse
F(x)=5x is injective with f: N-
- injective
- Not surjective
- inverse
- surjective
If the image of a function f: A-B equals its range, the function is surjective (onto).
- a bijective
- a composition
- a invertible
- a associative
F is bijective because it has both surjective and injective properties.
- one to one
- into
- one too many.
- onto
The function (gof) is also onto if f and g are.
- an associative property
- a commutative property
- a one-to-one function
- Both A and B may be
Composition does not have commutative property, but it always has associative property.
- 6x+8
- 6x+3
- 6x+7
- 6x+9
The formula f(g(x)) yields the composition of f and g as 2(3x + 4) + 1
- 4
- 2
- 8
- 1
- From R to R, the function f(x) = x3 is a bijection.
- From the set of integers to itself, the function f(x)=x+1 is onto.
- A and B both
- None of the preceding
The proverb "A and B are true" is true, as explained.
- Babylonians
- Konrad Zuse
- George Boole
- G. Cantor
The first method of handling symbolic logic was developed by George Boole and is now referred to as Boolean algebra.
- an Idempotent Law
- a Double Complement Law
- a Complement Law
- an Identity Law
A+A=A (OR Form) and A.A=A (AND Form) are examples of idempotent law.
- a Commutative Law
- an Absorption Law
- an Associative Law
- a Dominance Law
Rule of Dominance: A.0=0 (AND Form) and A.+1=1 (OR Form)
- minterm
- mixterm
- variables
- None of the above
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.
- 1952
- 1950
- 1953
- 1956
Maurice Karnaughin introduced the Karnaugh map (K-map) first 1953.
- NOT
- XOR
- AND
- X-NOR
The X-NOR or Exclusive NOR gate is a type of logic gate that produces high output for identical inputs but low output otherwise.
- 5
- 2
- 3
- 4
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)
- 5
- 3
- 2
- 4
This is a function of degree 4 that transfers the set of ordered pairs of Boolean variables to the set "0, 1".
- Edge
- Nodes
- fields
- lines
A graph is made up of a collection of nodes or vertices connected by a collection of edges.
- a non-empty set of vertices
- an empty set of vertices
- Both A and B
- None of the above
A graph is made up of a set of edges (E) and a set of non-empty vertices (V).
- Degree of a vertex
- Handshaking Lemma
- Degree of a Graph
- None of the above
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.
- According to the Handshaking lemma, a vertex is referred to as an even vertex if its degree is even.
- The number of edges is equal to twice the sum of all the vertices' degrees.
- When a vertex's degree is odd, it is referred to as an odd vertex.
- A graph's degree is equal to its highest vertex degree.
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.
- No nodes exist in a null graph.
- No even or odd vertex exists in the null graph
No edges exist in the null graph
There are no edges in a null graph.
- Multi graph
- Simple graph
- Hamiltonian Graphs
- Euler Graphs
- Hamiltonian Graphs
- Directed Graph
- Planar graph
- Euler Graphs
If there is a closed trail that spans every edge of the connected graph, it is referred to as an Euler graph.
- 540
- 720
- 360
- 180
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.
- 35
- 36
- 37
- 38
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.
- greater than 3
- less than 5
- equal to 5
- More than 10
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.
- acyclic undirected graph
- cyclic undirected graph
- acyclic directed graph
- cyclic directed graph
A connected acyclic undirected graph is a tree.
- (N+1) Edges
- (N^2)-1 Edges
- N Edges
- (N-1) Edges
(N1) A number of edges make up a tree with N number of vertices.
- Root
- Leaf
- Internal node
- None of the above
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.
- Centers
- Bi- Centers
- Unlabeled
- labeled
A labeled tree is a tree whose vertices are each given a distinct number between 1 and n.
- O(log n)
- O(n)
- O(n^2)
- O(nlog n)
The average complexity for insertion is O(log n), and the worst case is O(n).
- O(logn)
- O( n)
- O(n^2)
- O(nlog n)
Space complexity: O(n) in the worst case and O(n) in average complexity. - 122. How many k numbers of vertices labeled trees are there?
- k^(n-2)
- k^(n-1)
- k^(n)
- k^(2)
The number of labeled trees with k vertices is equal to k(n-2).
- TRUE
- FLASE
- either true or false
- cannot be determined
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.
- A tree with n leaves and a single internal vertex
- A tree with n vertices and n-1 cycles is option B.
- A tree with n vertices in a straight line.
- A tree with 0 or more connected subtrees
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.
- Bi-Centers
- Central Tree
- Rooted Tree
- Labeled Trees
Bi-central trees are those that only have two or more centers.
- 1638
- 1674
- 1654
- 1666
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.
- Sample Space
- Event
- Random Experiment
- Tossing Space
Sample Room The sample space is the set S of all potential outcomes when we experiment.
- 4
- 1
- 3
- 2
When a coin is tossed, one of two possible results is possible: heads or tails.
- (1/6)
- (5/6)
- (2/3)
- (1/3)
Any one of the numbers has a 1/6 probability
- (1/52)
- (1/13)
- (3/52)
- (1/26)
Find the likelihood of drawing an ace if one card is chosen at random from a deck of 52 cards...
- (1/6)
- (3/26)
- (1/13)
- (1/4)
- discrete variables
- probability function
- data
- machine
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.
- 10
- 20
- 5
- 15
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.
- (1/5)
- (1/25)
- (1/10)
- (1/20)
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.
- 0.42
- 0.423
- 0.421
- 0.422
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. Next TopicWhat is Ethical Hacking |