Use the laws of propositional logic to prove each of the following assertions. Start by defining a generic conditional statement p → q, and then restate the assertion as the equivalence or non-equivalence of two propositions using p and q. Finally prove that the two propositions are equivalent or non-equivalent. For example, the statement: "A conditional statement is not logically equivalent to its converse" is proven by showing that that p → q is not logically equivalent to q → p.