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Question
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]
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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.
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