If p: 16 is a factor of 256 and q: 324 is a perfect square, then ∼ p Leftrightarrow ∼ q is equivalent to

Question

If p: 16 is a factor of 256 and q: 324 is a perfect square, then ∼ p Leftrightarrow ∼ q is equivalent to (A) p ∧ q (B) (∼ p) ∧ q (C) p ∧(∼ q) (D) Both(b) and (c)

Tardigrade Admin · Accepted Answer

According to statements given, p is true and q is true. So, ∼ p is false and ∼ q is false ∴ ∼ p Leftrightarrow ∼ q is true. Now, p ∧ q is true. (∼ p) ∧ q is false. p ∧(∼ q) is false. ∼ p Leftrightarrow ∼ q is equivalent to p ∧ q.

Q. If $p : 16$ is a factor of 256 and $q : 324$ is a perfect square, then $\sim p \Leftrightarrow\sim q$ is equivalent to

$p \land q$

$(\sim p) \land q$

$p \land (\sim q)$

Both(b) and (c)

According to statements given, $p$ is true and $q$ is true.
So, $\sim p$ is false and $\sim q$ is false
$∴ \sim p \Leftrightarrow\sim q$ is true.
Now, $p \land q$ is true.
$(\sim p) \land q$ is false.
$p \land (\sim q)$ is false.
$\sim p \Leftrightarrow\sim q$ is equivalent to $p \land q$ .

Q. If p:16 is a factor of 256 and q:324 is a perfect square, then ∼p⇔∼q is equivalent to

p∧q

(∼p)∧q

p∧(∼q)