Question:
If the Boolean expression $(\mathrm{p} \Rightarrow \mathrm{q}) \Leftrightarrow(\mathrm{q} *(\sim \mathrm{p}))$ is a tautology, then the Boolean expression $\mathrm{p} *(\sim \mathrm{q})$ is equivalent to
Correct Option: 1,
Solution:
$\because p \rightarrow q \equiv \sim p \vee q$
$\mathrm{So}, * \equiv \mathrm{v}$
Thus, $\mathrm{p}^{*}(\sim \mathrm{q}) \equiv \mathrm{pv}(\sim \mathrm{q})$
$\equiv \mathrm{q} \rightarrow \mathrm{p}$