Question

$~(p\Rightarrow q)\iff ~p\vee ~q$ is

• A. A tautology
• B. A contradiction
• C. Neither a tautology nor a contradiction
• D. Cannot come to any conclusion

Answer 1

The correct option is C

Neither a tautology nor a contradiction

Explanation for the correct option:

Finding $~(p\Rightarrow q)\iff ~p\vee ~q$ is

$p$	$q$	$~p$	$~q$	$p\Rightarrow q$	$~\left(p\Rightarrow q\right)$	$~p\vee ~q$	$~\left(p\Rightarrow q\right)\iff ~p\vee ~q$
T	T	F	F	T	F	F	T
T	F	F	T	F	T	T	T
F	T	T	F	T	F	T	F
F	F	T	T	T	F	T	F

For a statement to be tautology the last column should have only true values.

Since the last column has false values too, therefore the statement is not a tautology.

For a statement to be contradiction the last column should have only false values.

Since the last column has true values too, therefore the statement is not contradiction.

Therefore,the statement is neither tautology nor contradiction.

Hence the correct option is (C).