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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