Question

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

Answer 1

$(p \to r) \land (q \to r) = (\lnot p \land r) \land (\lnot q \land r) = (\lnot p \land \lnot q) \land (r \land r)=$

$=\lnot (p \lor q) \land r=(p \lor q) \to r$