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

Exercise 5.1 · Q16

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: B = (A\capB)\cup(A'\capB).

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$A\cap B = \{3,4\}$ (computed above). $A' = X-A = \{5,6,7,8,9,10\}$ , so $A'\cap B = \{5,6,7,8,9,10\}\cap\{3,4,5,6\} = \{5,6\}$ . Union: $(A\cap B)\cup(A'\cap B) = \{3,4\}\cup\{5,6\} = \{3,4,5,6\} = B$ . Verified — B splits cleanly into …

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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: B = (A∩B)∪(A'∩B).

Concept understanding — Union of Sets

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: B = (A∩B)∪(A'∩B).

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