How can we prove that following proposition is a tautology with the help of logical equivalence?
$$[(r\lor{p})\rightarrow(r\lor{q})]\leftrightarrow[(r\lor(p\rightarrow{q})]$$
I can prove these types of statements but this proposition becomes too complicated and long when i try to solve it. I got help from book and online examples but those are all simple propositions not as complicated as this.
HINT
Use the Implication equivalence:
$$p \to q \iff \neg p \lor q$$
So for the left side:
$$(r \lor p) \to (r \lor q) \iff \neg (r \lor p) \lor (r \lor q) \iff (\neg r \land \neg p) \lor r \lor q \iff \neg p \lor r \lor q$$
You try the right side!