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 "If it rains I won't go to school, instead I will meet my friends." ?

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

Answer 1

The correct option is B $q\vee \sim r\Rightarrow \sim p$


$p:$ It rains today.
$q:$ I go to school.
$r:$ I shall meet my friends.
The given statement can be expressed as
$p\Rightarrow (\sim q\wedge r)$
There is no such expression in options.
So, we check it's contra-positive, that is
$\sim [p\Rightarrow (\sim q\wedge r\left)\right]$
or, $q\vee \sim r\Rightarrow \sim p$