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# If p : It rains today. q : I go to school. r : I shall meet my friends. s : I shall go for a movie. Then which of the following is the proportionate representation of the statement, If it does not rain or if I do not go to school, then I shall meet my friends and go for a movie.

$\begin {array} {1 1} (A)\;(^{\sim}p\: \wedge\: ^{\sim}q) \Rightarrow (r \wedge s) & \quad (B)\;^{\sim}(p \wedge q) \Rightarrow (r \wedge s) \\ (C)\;^{\sim}(p Vq)\Rightarrow (r V s) & \quad (D)\;None\: of\: these \end {array}$

Ans : (B)
$^{\sim}p$ : It does not rain today
$^{\sim}q$ : I do not go to school
$s$: I shall go to a movie
$r$: I shall meet my friends
The representation of I shall meet my friends and go for a movie = $r \wedge s$
The representation of it does not rain or I do not go to school= $\sim p \vee \sim q$
Therefore, $(^{\sim}p \vee ^{\sim}q) \Rightarrow (r \wedge s)$
edited Mar 20, 2014