Question

Prove that (p ∧ q) → (p ∨ q) is a tautology using the table of propositional

equivalences.

Answer 1

Using the following equivalence law (you can prove from a truth table):

$r\rightarrow s\equiv \lnot r\lor s$

Let $r = p\land q$ and $s = p\lor q$, then

$(p\land q)\rightarrow (p\lor q)\equiv \lnot(p\land q)\lor(p\lor q).$