91Ó°ÊÓ

Prove the distributive laws for propositional logic: If \(P, Q\) and \(R\) are statements, then a) \(P \vee(Q \wedge R) \equiv(P \vee Q) \wedge(P \vee R)\). b) \(P \wedge(Q \vee R) \equiv(P \wedge Q) \vee(P \wedge R)\).

Prove that \(\sqrt{10}\) is irrational.

Prove that the square root of any natural number is either an integer or irrational.