Which of the following is false?

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(D) We evaluate the statement $((p \wedge p)$ $\rightarrow q)$ $\rightarrow p$. Since $p \wedge p \equiv p$,the expression simplifies to $(p$ $\righta

Vedclass · Accepted Answer

$((p \wedge p)$ $\rightarrow q)$ $\rightarrow p$ is a tautology.

Vedclass · Answer

(D) We evaluate the statement $((p \wedge p)$ $\rightarrow q)$ $\rightarrow p$. Since $p \wedge p \equiv p$,the expression simplifies to $(p$ $\rightarrow q)$ $\rightarrow p$. If $p$ is $F$ (False) and $q$ is $T$ (True) or $F$ (False),then $(p \rightarrow q)$ is $T$. Then $(p$ $\rightarrow q)$ $\rightarrow p$ becomes $T \rightarrow F$,which is $F$. Since the statement can be false,it is not a tautology. Therefore,option $D$ is false.

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