Which of the following is correct statement? (a) $S_1:(p \wedge q) \equiv \sim(p \rightarrow \sim q)$. (b)…
Which of the following is correct statement?
(a) $S_1:(p \wedge q) \equiv \sim(p \rightarrow \sim q)$.
(b) $S_2:(p \wedge q) \wedge(\sim p v \sim q)$ is tautology.
(c) $\left.S_3:[p \wedge(p \rightarrow \sim q)] \rightarrow q\right)$ is contradiction.
(d) $S_4: p \rightarrow(q \rightarrow p)$ is contingency.
Statement $S_3$ is correct,
Statement $S_1$ is correct,
Statement $S_1$ and $S_2$ are correct,
Statement $S_4$ is correct,
Solution
$\begin{aligned}
& \because \sim(p \rightarrow q) \equiv p \wedge \sim q \\
& \Rightarrow \sim(p \rightarrow \sim q) \equiv p \wedge \sim(\sim q) \equiv p \wedge q
\end{aligned}$
Hence, $S_1$ is correct