Prove that (p ∧ q) → (p ∨ q) is a tautology using the table of propositional
equivalences.
Using the following equivalence law (you can prove from a truth table):
r→s≡¬r∨sr\rightarrow s\equiv \lnot r\lor sr→s≡¬r∨s
Let r=p∧qr = p\land qr=p∧q and s=p∨qs = p\lor qs=p∨q, then
(p∧q)→(p∨q)≡¬(p∧q)∨(p∨q).(p\land q)\rightarrow (p\lor q)\equiv \lnot(p\land q)\lor(p\lor q).(p∧q)→(p∨q)≡¬(p∧q)∨(p∨q).
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