Which of the following is a fallacy?

(p \land q) \land \sim (p \lor q)

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p \lor (\sim p \land q)

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(p \Rightarrow q) \Rightarrow p

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None of these

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Solution

The correct option is A $(p \land q) \land \sim (p \lor q)$
$(p \land q) \land \sim (p \lor q) = (p \land q) \land (\sim p \land \sim q) [∵ \sim (p \lor q) = \sim p \land \sim q] = (p \land \sim p) \land (q \land \sim q)$
$(p \land \sim p)$ and $(q \land \sim q)$ are always false.
$∴ (p \land \sim p) \land \sim (p \lor q)$ is false for all values of p and q.
Hence, it is a fallacy.

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(S_{1}) : (q \lor p) \to (p \leftrightarrow\sim q)

(S_{2}) :\sim q \land (\sim p \leftrightarrow q)

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