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

Question

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

(1) →, →

(2) ∧, ∨

(3) ∨, →

(4) ∧, →

Answer 1

Option 1 is Correct ( →, →)

 

( p ∧ q ) → ( p → q )

 ( p ∧ q ) → ( ∼ p ∨ q ) 

 ( ∼ p ∨ ∼ q ) ∨ ( ∼ p ∨ q ) 

∼ p ∨ ( ∼ q ∨ q ) ⇒ 

Tautology ⇒ ⊙ ⇒→ 

 ⊗ ⇒→