Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 2 - Set Theory - 2.4 Set Operations and Venn Diagrams with Three Sets - Exercise Set 2.4: 3

Answer

(A∪B)∩(A∪C) = {1,2,3,5,7}

Work Step by Step

A={1,3,5,7} B={1,2,3} C={2,3,4,5,6} TO FIND (A∪B)∩(A∪C) Let's first find (A∪B) and (A∪C) A∪B = {1,3,5,7} ∪ {1.2.3} = {1,2,3,5,7} (All elements of A and the elements of B which are not in A) A∪C = {1,3,5,7} ∪ {2,3,4,5,6} = {1,2,3,4,5,6,7} (All elements of A and the elements of C which are not in A) (A∪B)∩(A∪C) = {1,2,3,5,7} ∩ {1,2,3,4,5,6,7} = {1,2,3,5,7} (Common elements of (A∪B) and (A∪C)) Thus (A∪B)∩(A∪C) = {1,2,3,5,7}
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