Consider the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B, if A S B then BC S AC. Use an element argument to construct a proof for the statement by putting selected sentences from the following scrambled list in the correct order. By definition of complement, x € B. Hence, x € A, because A N B = Ø. Suppose A and B are any sets such that A S B, and suppose x E B. Therefore, by definition of complement x E A°, and thus, by definition of subset, BC C AC. Suppose A and B are any sets such that A C B, and suppose x E BC. If x were in A, then x would have to be in B by definition of subset. But x € B, and so x € A. Proof: 1. ---Select--- 2. --Select--- 3. -Select--- 4. ---Select---

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