Using truth table prove that : p q=(p q) ( p q) - Vidyadip

Question

Using truth table prove that : $p \leftrightarrow q=(p \wedge q) \vee(\sim p \wedge \sim q)$

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Answer

1	2	3	4	5	6	7	8
1	2	3	A	5	6	B	8
P	q	$p \leftrightarrow q$	$p \wedge q$	$\sim p$	$\sim q$	$\begin{gathered}\sim p \wedge \\ \sim q\end{gathered}$	$A \vee B$
T T F F	T F T F	T F F T	T F F F	F F T T	F T F T	F F F T	T F F T

By column number 3 and 8
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

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