The following are invalid arguments. Explain what is wrong with them. (a) Let A(x) be x can fly. Given the premise xA(x), we conclude that A(George). Therefore, George can fly. (b) All rabbits like fruit. George is not a rabbit. Therefore, George does not like fruit. (c) Let L(x, y) be x loves y. Given the premise xL(x, George), it follows that L(George, George). Then by Existential Generalization it follows that xL(x, x), so that someone loves themselves.

Let x and y be real numbers. Use a proof by contraposition to show that if x + y 2, then x 1 or y 1.