Which of the following is logically equivalent to \[\sim(\s... | MATH - MATHEMATICAL LOGIC | SolveeIt | Solveeit

Today, August 23

Question

Which of the following is logically equivalent to

$\sim(\sim p \Rightarrow q)$

A

$p \land q$

B

$p \land \sim q$

C

$\sim p \land q$

D

$\sim p\mspace{6mu} \land \sim q$

Answer

$\sim p\mspace{6mu} \land \sim q$

Explanation

Solution

Since $\sim(p \Rightarrow q) \equiv p\mspace{6mu} \land \sim q$

$\sim(\sim p \Rightarrow q) = \mspace{6mu}\sim p\mspace{6mu} \land \sim q$