[p (p q)] - Vidyadip

MCQ

$\sim[p \rightarrow(p \wedge \sim q)] \equiv$

A
$p$
B
$q$
✓
$(p \wedge q)$
D
$(p \vee q)$

✓

Answer

Correct option: C.

$(p \wedge q)$

$\sim[p \rightarrow(p \wedge \sim q)]$
$=\sim[\sim p \vee(p \wedge \sim q)] ($implication equivalence$)$
$=p \wedge \sim(p \wedge \sim q) ($De Morgan's law$)$
$=p \wedge(\sim p \vee q) ($De Morgan's law$)$
$=(p \wedge \sim p) \vee(p \wedge q) ($Distributive law$)$
$=F \vee(p \wedge q) ($Complement law$)$
$=p \wedge q ($Identity law$)$

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