JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Negation of Compound Statements

We have learnt about negation of a simple statement. Writing the negation of compound statements having conjunction, disjunctions, implication, equivalence, etc, is not very simple. So, let us discuss the negation of compound statement.

(i) Negation of conjuntion :

If p and q are two statements, then \[\tilde{\ }(p\wedge q)\equiv (\tilde{\ }p\,\vee \tilde{\ }q)\]

(ii) Negation of disjuntion :

If p and q are two statements, then \[\tilde{\ }(p\vee q)\equiv (\tilde{\ }p\,\wedge \tilde{\ }q)\]

(iii) Negation of implication :

If p and q are two statements, then \[\tilde{\ }(p\Rightarrow q)=(p\,\wedge \tilde{\ }q)\]          

(iv) Negation of biconditional statement or equivalence :

If p and q are two statements, then

\[\tilde{\ }(p\Leftrightarrow q)=(p\wedge \tilde{\ }q)\vee (q\wedge \tilde{\ }p)\]