Question

Prove the following equivalences by the logical derivation: 

(b) (p ∧ q) → r ≡ (p → r) ∨ (q → r)

Answer 1

1) $((p\land q)\to r) \iff (\lnot (p\land q) \lor r) \iff$

$\iff (\lnot p \lor \lnot q \lor r)$

2) $((p\to r) \lor (q\to r)) \iff ((\lnot p \lor r) \lor (\lnot q \lor r))$

$((\lnot p \lor r) \lor (\lnot q \lor r)) \iff (\lnot p \lor \lnot q \lor r)$

we obtained two equal terms, which means, that statement is true