Negation of $$(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$$ is :
JEE · Math · previous-year question
- A.$$(\sim q) \wedge p$$
- B.$$q \wedge(\sim p)$$correct
- C.$$p \vee(\sim q)$$
- D.$$(\sim p) \vee q$$
Answer
B. $$q \wedge(\sim p)$$
Explanation
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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