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 · Q20

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: n(B) = n(A'\capB) + n(A\capB).

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$A' = X-A = \{5,6,7,8,9,10\}$ , so $A'\cap B = \{5,6,7,8,9,10\}\cap\{3,4,5,6\} = \{5,6\}$ , giving $n(A'\cap B) = 2$ . Also $A\cap B = \{3,4\}$ , so $n(A\cap B) = 2$ . Sum: $n(A'\cap B)+n(A\cap B) = 2+2 = 4$ . Directly, $n(B) = n(\{3,4,5,6\}) = 4$ . Both equal 4, verifying the identity (the printed statement omits the 'n(' b …

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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: n(B) = n(A'∩B) + n(A∩B).

Concept understanding — Practical Problems on Union and Intersection of Two 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: n(B) = n(A'∩B) + n(A∩B).

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