Question

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

• A. $q \Rightarrow p$
• B. $\sim q \Rightarrow p$
• C. $p \Rightarrow \sim q$
• D. $p \Rightarrow q$

Answer 1

Answer: (A)

$\because p \rightarrow q \equiv \sim p \vee q$
So, $* \equiv v$
Thus, $p ^{*}(\sim q ) \equiv pv (\sim q )$
$\equiv q \rightarrow p$