EXERCISE 1.4Q 3.6 PAGE 11
Exercise 1.4 | Q 3.6 | Page 11
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
SOLUTION
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
≡ ~ [T ∨ (F ∧ F)] ∧ ~ [(F ∧ ~ F) ∧ T]
≡ ~ (T ∨ F) ∧ ~ [(F ∧ T) ∧ T]
≡ ~ T ∧ ~ (F ∧ T)
≡ F ∧ ~ F
≡ F ∧ T
≡ F
Hence, truth value is F.