Consider the following statement. (Assume that all sets are subsets of a universal set U.)For all sets A, B, and C, if A C B and BnC = Ø then AnC = Ø.Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set.Then by definition of intersection and complement A = U.Then (An C) = U.By definition of intersection x E A and x € C.Hence x e B n c by definition of intersection.Therefore A B.Thus BnC + Ø by definition of Ø.Then x E B because A C B. In addition, we know that x e C.Proof by contradiction:1. Suppose that there exists sets A, B, and C such that AC B, and BnC = 0 and AnC+ 0.2. Then there exists an element x such that x E ANc.3. ---Select--4. ---Select---5. ---Select--6. ---Select--7. But this contradicts the supposition. Hence the supposition is false, and so AnC = 0.

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For all sets A, B, and C, if A C B and BnC = 0 then An C = 0. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set. Then by definition of intersection and complement A = U. Then (An c) = U. By definition of intersection x E A and x e C. Hence x e BN c by definition of intersection. Therefore A B. Thus BnC+ O by definition of Ø. Then x E B because AC B. In addition, we know that x€C. Proof by contradiction: 1. Suppose that there exists sets A, B, and C such that A C B, and BnC = 0 and A n C + 0. 2. Then there exists an element x such that x E ANC. 3. -Select- 4. ---Select- 5. --Select- 6. --Select--- 7. But this contradicts the supposition. Hence the supposition is false, and so AnC = 0.