Question

If $p$'s truth value is $T$ and $q$'s truth value is $F$, then which of the following have the truth value $T$?
(i) $p\vee q$
(ii) $\sim p\vee q$
(iii) $p\vee (\sim q)$
(iv) $p\wedge (\sim q)$

• A. (i), (ii), (iii)
• B. (i), (iii), (iv)
• C. (i), (ii), (iv)
• D. (ii), (iii), (iv)

Answer 1

The correct option is B (i), (iii), (iv)

Given $p^{\prime }s$ truth value is $T$ and $q^{\prime }s$ truth value is $F$.

We have to determine which of the given have the truth value $T$.

$\left(i\right)p\vee q$

$p$	$q$	$p\vee q$
$T$	$F$	$T$

$\left(ii\right)\sim p\vee q$

$p$	$\sim p$	$q$	$\sim p\vee q$
$T$	$F$	$F$	$F$

$\left(iii\right)p\vee (\sim q)$

$p$	$q$	$\sim q$	$p\vee (\sim q)$
$T$	$F$	$T$	$T$

$\left(iv\right)p\wedge (\sim q)$

$p$	$q$	$\sim q$	$p\wedge (\sim q)$
$T$	$F$	$T$	$T$

From the above tables we see that, $\left(i\right),\left(iii\right),\left(iv\right)$ have truth value $T$.