Truth table, Negation, Conjunction

1.4.2 Truth Table

A table showing the truth value of a statement formula is called truth table.

1.4.3 Negation

Letp be any simple statement, then the negation of p is formed by writing "It is false that" before p or introducing the word "not" at the proper place. The negation of pis also obtained by writing "p is false". The negation of p is denoted by - p p or

the statement p is true, then p is false and if p is false then - p is true.

The truth table for negation of p is given below

 

Examples :

Sr. No.

Statement p

~P

 

p : A tharva is intelligent boy

K ;

 ~p : A tharva is not intelligent boy OR

It is false that Atharva is intelligent boy

2.

p : Delhi is the capital of India

~ p : Delhi is not the capital of India OR

It is false that Delhi is the capital of India OR

It is not the case that Delhi is the capital of India

Note : p is the unary connective as only one statement is required to form

negation.

1.4.4 Conjunction

A compound statement which is obtained by combining two primary statements by

using the connective "and" is called conjunction i.e. the conjunction of two statements p and q is the statement p n q. It is read as "p and q" or "p meet q".

The statement p A q has the truth value T whenever both p and q have the truth value T, otherwise p A q has the truth value F.