Given that p is ‘false’ and q is 'true' then the statement which … - Vidyadip

MCQ

Given that p is ‘false’ and q is 'true' then the statement which is 'false' is

✓
$\sim \mathrm{p} \rightarrow \sim \mathrm{q}$
B
$p \rightarrow(q \wedge p)$
C
$p \rightarrow \sim q$
D
$q \rightarrow \sim p$

✓

Answer

Correct option: A.

$\sim \mathrm{p} \rightarrow \sim \mathrm{q}$

(A)
$\begin{array}{l}\sim p \rightarrow \sim q \equiv \sim F \rightarrow \sim T \equiv T \rightarrow F \equiv F \\ p \rightarrow(q \wedge p) \equiv F \rightarrow(T \wedge F) \equiv F \rightarrow F \equiv T \\ p \rightarrow \sim q \equiv F \rightarrow \sim T \equiv F \rightarrow F \equiv T \\ q \rightarrow \sim p \equiv T \rightarrow \sim F \equiv T \rightarrow T \equiv T\end{array}$

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