If the Boolean expression

Question:

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

  1. $\mathrm{q} \Rightarrow \mathrm{p}$

  2. $\sim \mathrm{q} \Rightarrow \mathrm{p}$

  3. $\mathrm{p} \Rightarrow \sim \mathrm{q}$

  4. $p \Rightarrow q$


Correct Option: 1

Solution:

$\because \mathrm{p} \rightarrow \mathrm{q} \equiv \sim \mathrm{p} \vee \mathrm{q}$

$\mathrm{SO}, * \mathrm{~V}$

Thus, $p^{*}(\sim q) \equiv p v(\sim q)$

$\equiv q \rightarrow p$

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