Solution to Show that (p → q) ∧ (p → r) and p → (q ∧ r) … - Sikademy
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Archangel Macsika

Show that (p → q) ∧ (p → r) and p → (q ∧ r) are logically equivalent using logical equivalence laws.

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From the left hand side,

(p\rightarrow q)\land(p\rightarrow r)\equiv(\neg p\lor q)\land(\neg p\lor r) (by reduction of \rightarrow )

\equiv\neg p\lor(q\land r) (by idempotence of \lor )

\equiv p\rightarrow(q\land r) (by reduction of \rightarrow )

Therefore, (p\rightarrow q)\land(p\rightarrow r)\space and \space p\rightarrow(q\land r) \\

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Question ID: mtid-5-stid-8-sqid-283-qpid-170