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Exercise 5.1 · Q17

Q.If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify: (A∪B) = (A−B) ∪ (A∩B) ∪ (B−A).

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A−B={1,2,3,4}−{3,4,5,6}={1,2}A-B = \{1,2,3,4\}-\{3,4,5,6\} = \{1,2\} (elements only in A). A∩B={3,4}A\cap B = \{3,4\} (elements in both). B−A={3,4,5,6}−{1,2,3,4}={5,6}B-A = \{3,4,5,6\}-\{1,2,3,4\} = \{5,6\} (elements only in B). Union of the three: {1,2}∪{3,4}∪{5,6}={1,2,3,4,5,6}\{1,2\}\cup\{3,4\}\cup\{5,6\} = \{1,2,3,4,5,6\}. Directly, A∪B={1,2,3,4}∪{3,4,5,6}={1,2,3,4,5,6}A\cup B = \{1,2,3,4\}\cup\{3,4,5,6\} = \{1,2,3,4,5,6\}. Both match, confirming …

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