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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

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


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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 by thanvigandhi_1

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