is opposite to that of p . It is denoted by p , read as not p . The truth value of p is T , if p is F , otherwise it is F . ( ) Let p and q be any two simple statements.
The conjunction of p and q is obtained by connecting p and q by the word and . It is denoted by p , read as ‘ p conjunction q ’ or ‘ p hat q ’. The truth value of p is T , whenever both p and q are T and it is F otherwise. ( ) The disjunction of any two simple statements p and q is the compound statement obtained by connecting p and q by the word ‘or’.
It is denoted by p , read as‘ p disjunction q ’ or ‘ p cup q ’.The truth value of p is F , whenever both p and q are F and it is T otherwise. ( ) The conditional statement of any two statements p and q is the statement, ‘If p , then q ’ and it is denoted by p . The statement p has a truth value F when q has the truth value F and p has the truth value T ; otherwise it has the truth value T. ( ) The bi-conditional statement of any two statements p and q is the statement ‘ p if and only if q ’ and is denoted by p ↔ The statement p ↔ has the truth value T whenever both p and q have identical truth values; otherwise has the truth value F .
( ) A statement is said to be a tautology if its truth value is always T irrespective of the truth values of its component statements. It is denoted by 𝕋 . - - Discrete Mathematics ( ) A statement is said to be a contradiction if its truth value is always F irrespective of the truth values of its component statements. It is denoted by 𝔽 .