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Implication

If p →∼ p ∨∼ ...

Question

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

F, F

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T, T

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F, T

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T, F

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Solution

The correct option is B $T, T$

$p$ $q$ $(\sim p \lor \sim q)$ $p \to (\sim p \lor \sim q)$

$T$
$T$
$F$
$F$ $T$
$F$
$T$
$F$ $F$
$T$
$T$
$T$ $F$
$T$
$T$
$T$

So, from above truth table $p \to (\sim p \lor \sim q)$ will be $F$ , if $p and q$ are $T and T$ respectively.

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$p$	$q$	$(\sim p \lor \sim q)$	$p \to (\sim p \lor \sim q)$
$T$ $T$ $F$ $F$	$T$ $F$ $T$ $F$	$F$ $T$ $T$ $T$	$F$ $T$ $T$ $T$