Which of the following is false?

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(C) tautology is a statement that is always true,while a contradiction is always false.$1$. $p \vee (\sim p)$: This is the law of excluded middle,whic

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$(p$ $\Rightarrow q) \Leftrightarrow (q$ $\Rightarrow p)$ is a tautology.

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(C) tautology is a statement that is always true,while a contradiction is always false.$1$. $p \vee (\sim p)$: This is the law of excluded middle,which is always true (tautology).$2$. $\sim (\sim p) \Leftrightarrow p$: This is the law of double negation,which is always true (tautology).$3$. $(p$ $\Rightarrow q) \Leftrightarrow (q$ $\Rightarrow p)$: This is false because the converse of an implication is not logically equivalent to the implication itself. For example,if $p$ is true and $q$ is false,$(T \Rightarrow F)$ is $F$,while $(F \Rightarrow T)$ is $T$. Since $F \Leftrightarrow T$ is false,this is not a tautology.$4$. $p \wedge (\sim p)$: This is the law of contradiction,which is always false (contradiction).Therefore,option $C$ is the false statement.

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