Answer to Question #294307 in Discrete Mathematics for Ayan

Question

~p →~q

~p v {p^q) can get your best answer for this??

Please answer this question.

Answer 1

The formula $\sim p →\sim q$ is equivalent to $q\to p$ according to contraposition law, and hence $q\to p$ is the best representation of $\sim p →\sim q.$

The formula $\sim p \lor (p\land q)$ is equivalent to $(\sim p \lor p)\land (\sim p\lor q)$, and hence to $T\land (\sim p\lor q),$ and thus to $\sim p\lor q.$ The last formula is equivalent to $p\to q,$ and hence $p\to q$ is the best representation of $\sim p \lor (p\land q).$