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Verify that each of the following is a logical implication by showing that it is impossible for the conclusion to have the truth value 0 while the hypothesis has the truth value 1.
(a) (p ∧ q) → p
(b) p (p ∨ q)
(c) [(p ∨ q)∧ ¬ p] → q
(d) [(p → q) ∧ (r → s) ∧ (p ∨ r)] → (q ∨ s)
(e) [(p → q) ∧ (r → s) ∧ (¬ q ∨ ¬ s)] → (¬p ∨ ¬r) |
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