If (p ∧ ~ q) ∧ (p ∧ r) → ~ p ∨ q is false, then the truth values of...

So, \left(p ∧ ~ q\right) ∧ \left(p ∧ r\right) \to ~ p ∨ q$</p><p>Taking Option \left(A\right): \left(T ∧ F\right) ∧ \left(T ∧ T\right) \to F ∨ T$

$≡ \left(F ∧ T\right) \to T$

$≡ F \to T ≡ T$

Hence, option \left(A\right)$is false.</p><p>Taking Option \left(B\right): \left(F ∧ F\right) ∧ \left(F ∧ F\right) \to T ∨ T$

$≡ F \to T ≡ T$

Hence, option \left(B\right)$is false.</p><p>Taking Option \left(C\right): \left(T ∧ T\right) ∧ \left(T ∧ T\right) \to F ∨ F$

$≡ T \to F ≡ F$

Hence, option \left(C\right)$is correct.</p><p>Taking Option \left(D\right): \left(F ∧ T\right) ∧ \left(F ∧ F\right) \to T ∨ F$

$≡ F ∧ F \to T$

$≡ F \to T ≡ T$

Hence, option \left(D\right) is false.