Let’s consider algebras with the following axioms in addition to commutativity and associativity: $$x \vee x=x$$ $$\neg \neg x = x$$
Does the Huntington axiom ( $\neg (\neg x \vee y) \vee \neg (\neg x ∨ \neg y) = x$ ) follow from the axioms? If yes prove it by showing how the axioms entail it, if not, give an interpretation that contradicts it, but satisfies the axioms above together with the commutativity and associativity axioms.
This is a homework assignment for my AI class, but I have no idea where to start. Could you give me some pointers?