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Negation

Prove: p⟷ q ...

Question

Prove:
$p ⟷ q \equiv\sim (p \land \sim q) \land (q \land \sim p)$

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Solution

$p ⟷ q \equiv\sim (p \land \sim q) \land (q \land \sim p)$
P V $\sim V$ $P \land \sim V = r$ $\sim p$ $V \land \sim P = r$ $\sim r$
T T F F F F T
T F T T F F F
F T F F T T T
F F T F T F T
$p ⟷ q$
$- r$ $s$ $r \land s$
T F F
F F T
T T T
T F F

P $\sim P$ $V$ $\sim P \land V$
T F T F
T F F T
F T T T
F T F F
Hence Proved.

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