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Tautology

If p∧∼ q∧ p...

Question

If $(p \land \sim q) \land (p \land r) \to\sim p \lor q$ is false,then the truth values of $p, q$ and $r$ are, respectively.

F, T, F

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T, F, T

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F, F, F

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T, T, T

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Solution

The correct option is A $T, F, T$
The truth table for the $(p \land \sim q) \land (p \land r) \to\sim p \lor q$ is false

p q r $\sim p \lor q$
1 1 1 1
1 0 1 0
1 1 0 1
1 0 0 0
0
1 1 1
0 0 1 1
0 1 0 1
0 0 0 1
only possible solutions of (p,q,r) is (T,F,T) or (T,F,F)

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