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.