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If p and q are true and r and s are false, find the truth value of the following compound statement. [(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]

EXERCISE 1.4Q 3.5    PAGE 11
Exercise 1.4 | Q 3.5 | Page 11

If p and q are true and r and s are false, find the truth value of the following compound statement.

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]


SOLUTION

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]

≡ [(T ∨ F) → F] ∨ ~[~ (T → T) ∨ F] 

≡ (T → F) ∨ ~ (~ T ∨ F)

≡ F ∨ ~ (F ∨ F)

≡ F ∨ ~ F

≡ F ∨ T

≡ T

Hence, truth value is T.

Mathematical Logic