If the Boolean expression ( p ∧ q ) ⊛ ( p ⊗ q ) is a tautology, then ⊛ and ⊗ are respectively given by

Step-by-step solution

Option A ( p ∧ q ) → ( p → q ) We know that a → b = ~ a ∨ b = ( p ∧ q ) ⟶ ( ~ p ∨ q ) = ~ ( p ∧ q ) ∨ ( ~ p ∨ q ) Using De Morgan's Law i.e. ~ a ∧ b = ~ a ∨ ~ b , = ( ~ p ∨ ~ q ) ∨ ( ~ p ∨ q ) Using associative law and commutative law i.e. a ∨ b ∨ c = a ∨ b ∨ c   &   a ∨ b = b ∨ a , = ~ p ∨ ( ~ q ∨ q ) = ~ p ∨ t = t Option ( B ) ( p ∧ q ) &#87