Let * , □ ∈ ∧ , ∨ be such that the Boolean expression ( p * ~ q ) ⇒...

Let

* , □ \in { ∧ , ∨ }

be such that the Boolean expression

( p * ~ q ) ⇒ ( p □ q )

is a tautology. Then :

Options

A $* = ∨ , □ = ∧$
B $* = ∨ , □ = ∨$
C $* = ∧ , □ = ∨$
D $* = ∧ , □ = ∧$

Correct answer

C. $* = ∧ , □ = ∨$

Step-by-step solution

Let

( p ∧ ~ q ) \to ( p ∨ q )

is a tautology.

$p$	$q$	$~ q$	$p ∨ q$	$p ∧ ~ q$	\left(p ∧ ~ q\right) ⇒ \left(p ∨ q\right)
$T$	$T$	$F$	$T$	$F$	$T$
$T$	$F$	$T$	$T$	$T$	$T$
$F$	$T$	$F$	$T$	$F$	$T$
$F$	$F$	$T$	$F$	$F$	$T

All are true so it's a tautology.

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