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A-0-2-4-6-8-10-B-0-1-3-4-6-7-9-C-1-2-4-5-7-8-10-A-B-B-C-

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Question Number 245 by 123456 last updated on 25/Jan/15
A={0,2,4,6,8,10} B={0,1,3,4,6,7,9} C={1,2,4,5,7,8,10} ∣(A∪B)∩(B∪C)∣
$$\mathrm{A}=\left\{\mathrm{0},\mathrm{2},\mathrm{4},\mathrm{6},\mathrm{8},\mathrm{10}\right\} \\ $$$$\mathrm{B}=\left\{\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{9}\right\} \\ $$$$\mathrm{C}=\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{7},\mathrm{8},\mathrm{10}\right\} \\ $$$$\mid\left(\mathrm{A}\cup\mathrm{B}\right)\cap\left(\mathrm{B}\cup\mathrm{C}\right)\mid \\ $$
Answered by mreddy last updated on 17/Dec/14
A∪B={0,1,2,3,4,6,7,8,9,10} B∪C={0,1,2,3,4,5,6,7,8,9,10} (A∪B)∩(B∪C)={0,1,2,3,4,6,7,8,9,10} ∣(A∪B)∩(B∪C)∣=10
$$\mathrm{A}\cup\mathrm{B}=\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\} \\ $$$$\mathrm{B}\cup\mathrm{C}=\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\} \\ $$$$\left(\mathrm{A}\cup\mathrm{B}\right)\cap\left(\mathrm{B}\cup\mathrm{C}\right)=\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\} \\ $$$$\mid\left(\mathrm{A}\cup\mathrm{B}\right)\cap\left(\mathrm{B}\cup\mathrm{C}\right)\mid=\mathrm{10} \\ $$

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