Question

Solve it:-
$\left(p\to q\right)\to [\left(\sim p\to q\right)\to q]$

• A. Tautology
• B. Contradiction
• C. Contingent
• D. Not statement

Answer 1

The correct option is A Tautology

$Y=(p⟶q)⟶[(\sim p⟶q)⟶q]$

Method : TRUTH TABLE [ ALWAYS PREFERABLE]

$p$	$q$	$p⟶q$	$(\sim p⟶q)$	$[(\sim p⟶q)⟶q]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$

As the result is always TRUE $(i.e.1)$;

$(p⟶q)⟶[(\sim p⟶q)⟶q]$ is Tautology.

A. Tautology