If the Boolean expression (p ⇒ q) Leftrightarrow(q *(∼ p)) is a tautology, then the Boolean expression p *(∼ q ) is equivalent to :

Question

If the Boolean expression (p ⇒ q) Leftrightarrow(q *(∼ p)) is a tautology, then the Boolean expression p *(∼ q ) is equivalent to : (A) q ⇒ p (B) ∼ q ⇒ p (C) p ⇒ ∼ q (D) p ⇒ q

Tardigrade Admin · Accepted Answer

∵ p arrow q ≡ ∼ p ∨ q So, * ≡ v Thus, p *(∼ q ) ≡ pv (∼ q ) ≡ q arrow p

Q. If the Boolean expression $(p \Rightarrow q) \Leftrightarrow (q * (\sim p))$ is a tautology, then the Boolean expression $p * (\sim q)$ is equivalent to :

$q \Rightarrow p$

$\sim q \Rightarrow p$

$p \Rightarrow\sim q$

$p \Rightarrow q$

$∵ p \to q \equiv\sim p \lor q$
So, $* \equiv v$
Thus, $p^{*} (\sim q) \equiv p v (\sim q)$
$\equiv q \to p$

Q. If the Boolean expression (p⇒q)⇔(q∗(∼p)) is a tautology, then the Boolean expression p∗(∼q) is equivalent to :

q⇒p

∼q⇒p

p⇒∼q

p⇒q