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 · Q15

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

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$A\cap B = \{1,2,3,4\}\cap\{3,4,5,6\} = \{3,4\}$ . $B' = X-B = \{1,2,7,8,9,10\}$ , so $A\cap B' = \{1,2,3,4\}\cap\{1,2,7,8,9,10\} = \{1,2\}$ . Union: $(A\cap B)\cup(A\cap B') = \{3,4\}\cup\{1,2\} = \{1,2,3,4\} = A$ . Verified: every element of A either lies in B (captured by $A\cap B$ ) or lies outside B (cap …

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←Previous question · 5.1Q14 — If A = 1, 2, 3, 4, B = 3, 4, 5, 6, C = 4, 5, 6, 7, 8 and universal set…→Next question · 5.1Q16 — If A = 1, 2, 3, 4, B = 3, 4, 5, 6, C = 4, 5, 6, 7, 8 and universal set…

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 = (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: A = (A∩B)∪(A∩B').

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