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A Proposition or a statement or logical sentence is a declarative sentence which is either true or false.

Example1: The following statements are all propositions:

  • Jawaharlal Nehru is the first prime minister of India.
  • It rained Yesterday.
  • If x is an integer, then x2 is a +ve integer.

Example2: The following statements are not propositions:

  • Please report at 11 a.m. sharp
  • What is your name?
  • x2=13

Propositional Variables

The lower case letters starting from P onwards are used to represent propositions

Example: p: India is in Asia
                 q: 2 + 2 = 4

Compound Statements

Statements or propositional variables can be combined by means of logical connectives (operators) to form a single statement called compound statements.

The five logical connectives are:

Symbol Connective Name
~ Not Negation
And Conjunction
Or Disjunction
Implies or if...then Implication or conditional
If and only if Equivalence or biconditional

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