Let p, q, r be three logical statements. Cons | vedclass

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(C) Given $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$.Using the associative and idempotent laws,we have $S_{1} \equiv (\sim p \vee \sim p) \vee

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If $S_{2}$ is False,then $S_{1}$ is True

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(C) Given $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$.Using the associative and idempotent laws,we have $S_{1} \equiv (\sim p \vee \sim p) \vee (q \vee r) \equiv \sim p \vee (q \vee r)$.Given $S_{2}: p \rightarrow (q \vee r)$.Using the conditional law $p \rightarrow x \equiv \sim p \vee x$,we have $S_{2} \equiv \sim p \vee (q \vee r)$.Since $S_{1} \equiv S_{2}$,they always have the same truth value.Therefore,if $S_{2}$ is False,$S_{1}$ must also be False.Thus,the statement 'If $S_{2}$ is False,then $S_{1}$ is True' is $NOT$ true.

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

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