Consider the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B. if A C B

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Consider The Following Statement Assume That All Sets Are Subsets Of A Universal Set U For All Sets A And B If A C B 1 (61.01 KiB) Viewed 25 times

Consider the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B. if A C B then Bº CA Use an element argument to construct a proof for the statement by putting selected sentences from the following scrambled list in the correct order. • Therefore, by definition of complement 2 € Bº, and thus, by definition of subset, Bº CA. • Therefore, by definition of complement 2 E A°, and thus, by definition of subset, B° CA. • If I were in A, then a would have to be in B by definition of subset. But 2 € B, and so z & A. • Suppose A and B are any sets such that A C B, and suppose r e Bº. Suppose A and B are any sets such that A C B, and suppose I E A. Suppose A and B are any sets such that AC B, and suppose z E B. . By definition of complement, 2 & B. • Hence, 2A, because An B=0. Line 1 Suppose A and B are any set: Line2 By donition of complement Line3 If x were in Athen x would ha Line4 Therefore, by the definition of