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# If p, q, r are simple propositions with truth values T,F,T then the truth value of $[(^{\sim}p Vq) \wedge ^{\sim}r] \Rightarrow p$ is

$\begin {array} {1 1} (A)\;false & \quad (B)\;true \\ (C)\;true,\: if\: r\: is\: false & \quad (D)\; true,\: if\: q\: is\: true \end {array}$

Can you answer this question?

Ans : (B)
$^{\sim}p V q$ means $F V F = F, ^{\sim}r$ means $F,$
$(^{\sim}p V q)\wedge \: ^{\sim}r$ means $F$
So,$[(^{\sim} pVq) \wedge \: ^{\sim}r] \Rightarrow p$ means $T$ i.e, true
answered Jan 23, 2014