Question

$p:$ He is hard working.
$q:$ He will win.
The symbolic form of "If he will not win then he is not hard working", is

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

Answer 1

Answer: (C)

$(\sim q)\Rightarrow (\sim p)$

Given $p:$ He is hard working

and $q:$ He will win

we get $\sim p:$ He is not hard working

and $\sim q:$ He will not win

Now the given statement in the question is "If he will not win then he is not hard working"

For this conditional statement, the symbolic form is $(\sim q)\Rightarrow (\sim p)$