The logical statement (p $$ \Rightarrow $$ q) $$\Lambda $$ ( q $$ \Rightarrow $$ p) is equivalent to :
JEE · Math · previous-year question
- A.q
- B.$$ \sim $$pcorrect
- C.p
- D.$$ \sim $$q
Answer
B. $$ \sim $$p
Explanation
(p $$ \Rightarrow $$ q) $$\Lambda $$ ( q $$ \Rightarrow $$ p) $$ \equiv $$ $$\left( { \sim p \vee q} \right) \wedge \left( { \sim q \vee \sim p} \right)$$ $$ \equiv $$ $$ \sim p \vee \left( {q \wedge \sim q} \right)$$ $$ \equiv $$ $$ \sim $$p As $${q \wedge \sim q}$$ is a fallacy.
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