82

Proposition

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

---