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 ↔ (T ∧ F)] 

≡ ~(T ↔ F)

≡ ~ F

≡ T

Hence, truth value is T.