If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following. (p ∧ ∼ q) ∨ (∼ p ∧ q)

QUESTION

Miscellaneous Exercise 1 | Q 4.09 | Page 32

If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.

(p ∧ ∼ q) ∨ (∼ p ∧ q)

SOLUTION

(p ∧ ∼ q) ∨ (∼ p ∧ q) ≡ (T ∧ ∼ T) ∨ (∼ T ∧ T)

≡ (T ∧ F) ∨ (F ∧ T)

≡ F ∨ F

≡ F

Hence, truth value is F.