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 · Q18

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 \cap (BΔC) = (A\capB) Δ (A\capC).

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$B-C = \{3,4,5,6\}-\{4,5,6,7,8\} = \{3\}$ . $C-B = \{4,5,6,7,8\}-\{3,4,5,6\} = \{7,8\}$ . So $B\Delta C = (B-C)\cup(C-B) = \{3\}\cup\{7,8\} = \{3,7,8\}$ . Left side: $A\cap(B\Delta C) = \{1,2,3,4\}\cap\{3,7,8\} = \{3\}$ . Right side: $A\cap B = \{3,4\}$ and $A\cap C = \{1,2,3,4\}\cap\{4,5,6,7,8\} = \{4\}$ ; their symmetric difference is ${3,4}\Delta{4} = ({3,4}-{4} …

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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 ∩ (BΔC) = (A∩B) Δ (A∩C).

Concept understanding — Difference and Symmetric Difference 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 ∩ (BΔC) = (A∩B) Δ (A∩C).

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