Question

If $p\equiv$ "It rains today", $q\equiv$ "I go to school", $r\equiv$ "I shall meet my friends"
What can be concluded from "I will go to school and meet my friends if it doesn't rain today"?

• A. $\sim p\Rightarrow (q\wedge r)$
• B. $\sim p\Rightarrow (q\vee r)$
• C. $q\wedge r\Rightarrow p$
• D. $q\vee r\Rightarrow p$

Answer 1

The correct option is A $\sim p\Rightarrow (q\wedge r)$

$p:$ It rains today.
$q:$ I go to school.
$r:$ I shall meet my friends.
The given statement can be expressed as :
"If it doesn't rain today, then I will go to school and meet my friends."
This can be expressed mathematically as:
$\sim p\Rightarrow (q\wedge r)$