the wing tatemer Assume that all sets are subsets of a universal set U. For all sets A and B, if A CB then BC C AC. n element argument to construct a proof for the statement by putting selected sentences from the following sc Therefore, by definition of complement x E Aº, and thus, by definition of subset, BC C AC. Hence, x € A, because A N B = Ø. By definition of complement, x € B. Suppose A and B are any sets such that A C B, and suppose x E Bº. If x were in A, then x would have to be in B by definition of subset. But x € B, and so x€A. Suppose A and B are any sets such that A S B. and suppose x E B.

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