Consider the statement For all non-empty sets A and B, A x B = B x A = A = B. Complete a logical proof of the statement by showing containment both ways. Assume A x D = B X A for nonempty sets A and B. Now, order 5 of the following sentences so that they form a logical proof of the statement: A C B Choose from these sentences. Your Proof (showing containment left to right first): Suppose I E A x B Let A x B = B x A = A =B Let I E A For any b E B. (I, b) E A x B We have shown = ( A = D E B A X B = B X A = (z, b) E B x A and so IEB Therefore A C B Assuming A = B, let a E A and be B For the other direction, order S of the following sentences so that they form a logical proof of the statement: B C A Choose from these Your Proof (showing containment from right to left): A = B = AXB=B XA Assuming A = B, let a E A and be B A x B = B xA = (Q, y) E B x A and so YEA Suppose y E A x B For any G E A, (a, y) E A x B We have shown y E B = yE A Let y E B Therefore B C A Hence A = BSelection Task This LaTex proof picks the exact 5 sentences from your interactive image task: For A C B: 1. Suppose x E A 2. Let A x B = B x A => A = B 3. For any b E B. (x, b) EAX B 4. (x, b) E B X A - xEB 5. Therefore A C B\f