Which of the following is always true? - Vidyadip

MCQ

Which of the following is always true?

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

✓

Answer

Correct option: C.

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

(C)
$\begin{array}{l} p \rightarrow q \equiv \sim p \vee q \\ \therefore \quad \sim(p \rightarrow q) \equiv p \wedge \sim q\end{array}$

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