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

Show that (p → r) ∨ (q → r) and (p ∧ q) → r are logically equivalent.

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(p → r) 


(p → r) ∨ (q → r)

\equiv (\neg p\lor r) \lor (\neg q\lor r) \ \ \ \ \ \ \ (Implication)

\equiv \neg p\lor r \lor \neg q\lor r \ \ \ \ \ \ \

\equiv (\neg p \lor \neg q)\lor r \ \ \ \ \ \ \ (Distribution)

\equiv \neg ( p\land q)\lor r (De Morgan's Law)

\equiv ( p\land q) → r (Implication)

Hence proved ,

(p → r) ∨ (q → r) and ( p\land q) → r are logically equivalent.



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Question ID: mtid-5-stid-8-sqid-2830-qpid-1387