Let the operations * , ⊙ ∈ \ ∧ , ∨\ . If (p * q) ⊙ (p ⊙ ~ q) is a...

Given, the operations $* , ⊙ \in \left\{∧ , ∨\right\}$. If \left(p * q\right) ⊙ $\left(p ⊙ ~ q\right)$ is a tautology, then the ordered pair \left(* , ⊙\right)$is</p><p>We will check each option one by one,</p><p>For option$A, \text{put} * = ∨$and$⊙ = Λ$</p><p>We get, \left(p ∨ q\right) ∧ \left(p ∨ ~ q\right)$

$≡ p ∨ \left(q ∧ ~ q\right)$

$≡ p ∨ \left(c\right) ≡ p$ \left\{\text{where c is contradiction}\right\}$</p><p>Now for option$B: \text{put} * = ∨ , ⊙ = ∨$</p><p>We get, \left(p ∨ q\right) ∨ \left(p ∨ ~ q\right)$

$≡ p ∨ \left(q ∨ ~ q\right)$

$≡ p ∨ T$ \left\{\text{where T is tautology}\right\}$</p><p>$≡ T$</p><p> Hence \left(∨ , ∨\right)$ is the answer.