Question

If $p$: It rains today, $q$: I go to school, $r$: I shall meet any friends and $s$: I shall go for a movie, then which of the following is the proposition? If it does not rain or if I do not go to school, then I shall meet my friend and go to a movie,

• A. $~(p\wedge q)\Rightarrow (r\wedge s)$
• B. $~(p\wedge ~q)\Rightarrow (r\wedge s)$
• C. $~(p\wedge q)\Rightarrow (r\vee s)$
• D. None of these

Answer 1

The correct option is C

$~(p\wedge q)\Rightarrow (r\vee s)$

Explanation for correct option :

Given,

$p$ statement : It rains today.

$q$ statement : I go to school.

$r$ statement : I shall meet my friends.

$s$ statement : I shall go for a movie.

If it does not rain or if I do not go to school, then I shall meet my friend and go to a movie can be expressed as $(~p\vee ~q)\Rightarrow (r\wedge s)$

or $~(p\wedge q)\Rightarrow (r\wedge s)$

Hence Option (C) is correct.