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 · Q14

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\capB)' = A'\cupB'.

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$A \cap B = \{1,2,3,4\}\cap\{3,4,5,6\} = \{3,4\}$ , so $(A\cap B)' = X-\{3,4\} = \{1,2,5,6,7,8,9,10\}$ . Also $A' = \{5,6,7,8,9,10\}$ and $B' = \{1,2,7,8,9,10\}$ , so $A'\cup B' = \{1,2,5,6,7,8,9,10\}$ . Both sides equal {1,2,5,6,7,8,9,10} …

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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: (A∩B)' = A'∪B'.

Concept understanding — Complement of a 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∩B)' = A'∪B'.

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