Topic Consider the following theorem and proof. Theorem: If x is rational and y is irrational, then xy is irrational. Proof: Suppose x is rational and y is irrational. If xy is rational, then we have x = and xy = for some integers p, q, m, m 9 n and n (with q and n not equal to 0). It follows that y xy E|F|AIS Therefore, xy must be rational. mq np That implies y is rational which is a contradiction. Please answer the following three questions in your post for this module: 1. Find a specific counterexample to show that the theorem is false. 2. Explain what is wrong with the proof. 3. What additional condition on x in the hypothesis would make the conclusion true?