Which among the following statements is not a contradiction

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

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\sim (p \land q) \land p

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[(p \to q) \to p] \land \sim p

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

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Solution

The correct option is B $\sim (p \land q) \land p$
$\begin{matrix} p & q & p \land q & \sim p & \sim q & (p \lor \sim q) = x & \sim p \land x & (\sim p \land x) \land q & \sim (p \land q) & \sim (p \land q) \land p & \sim p \land \sim q = y & y \land (p \land q) & p \to q & (p \to q) \to p = t & t \land \sim p T & T & T & F & F & T & F & F & F & F & F & F & T & T & F T & F & F & F & T & T & F & F & T & T & F & F & F & T & F F & T & F & T & F & F & F & F & T & F & F & F & T & F & F F & F & F & T & T & T & T & F & T & F & T & F & T & F & F \end{matrix}$

Clealry from the above truth table except statement $\sim (p \land q) \land p$ all other given statements are contradictions.

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