Which of the following statements is a tautology?

We know,

A \to B ≡ ~ A ∨ B$</p><p>Now solving all options one by one we get,$

\left(A\right)p \to \left(p ∧ \left(p \to q\right)\right)$</p><p>$≡ \left(~ p\right) ∨ \left(p ∧ \left(~ p ∨ q\right)\right)

$≡ \left(~ p\right) ∨ \left(f ∨ \left(p ∧ q\right)\right)$

$≡ ~ p ∨ \left(p ∧ q\right) ≡ \left(~ p ∨ p\right) ∧ \left(~ p ∨ q\right)</p><p>$≡ ~ p ∨ q$</p><p>Which is not a tautology$

\left(B\right)\left(p ∧ q\right) \to \left(~ p \to q\right)

$≡ ~ \left(p ∧ q\right)$ ∨ \left(p ∨ q\right)$</p><p>$≡ ~ p ∨ ~ q ∨ \left(p ∨ q\right)

$≡ ~ p ∨ p ∨ ~ q ∨ q$

$≡ T ∨ T ≡ T$

Tautology</p><p>\left(C\right) \left(p ∧ \left(p \to q\right)\right) \to ~ q$</p><p>$≡ ~ \left(p ∧ \left(~ p ∨ q\right)\right) ∨ ~ q

$≡ ~ \left(p ∧ q\right)$ ∨ ~ q$</p><p>$≡ ~ p ∨ ~ q$</p><p>Which is not a tautology$

\left(D\right)$p ∨ \left(p ∧ q\right)$ ≡ p$</p><p>Which is not a tautology$