Negation of [(p q) (q p)] is :

Question

Negation of $$(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$$ is :

Accepted Answer

Given: $(p \rightarrow q) \rightarrow(q \rightarrow p)$

Negation of above statement is :

$$
\begin{aligned}
& \sim[(p \rightarrow q) \rightarrow(q \rightarrow p)] \\
& \equiv \sim[\sim p \rightarrow q \wedge q \rightarrow p] \\
& \equiv p \rightarrow q \wedge \sim q \rightarrow p \\
& \equiv \sim p \vee q \wedge q \wedge \sim p] \\
& \equiv q \wedge(\sim p)
\end{aligned}
$$

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