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 · Q11

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\cup(B\capC) = (A\cupB) \cap (A\cupC).

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$B \cap C = \{3,4,5,6\}\cap\{4,5,6,7,8\} = \{4,5,6\}$ . Left side: $A \cup (B\cap C) = \{1,2,3,4\} \cup \{4,5,6\} = \{1,2,3,4,5,6\}$ . Right side: $A \cup B = \{1,2,3,4,5,6\}$ and $A \cup C = \{1,2,3,4,5,6,7,8\}$ , so $(A\cup B)\cap(A\cup C) = \{1,2,3,4,5,6\}\cap\{1,2,3,4,5,6,7,8\} = \{1,2,3,4,5,6\}$ . Both sides equal {1,2,3,4,5, …

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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∩C) = (A∪B) ∩ (A∪C).

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∪(B∩C) = (A∪B) ∩ (A∪C).

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