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: 4

Answer

(A∩B)∪(A∩C) = {1,3,5}

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} = {1,3} (Common elements of A and B) A∩C = {1,3,5,7} ∩ {2,3,4,5,6} = {3,5} (Common elements of A and C) (A∩B)∪(A∩C) = {1,3} ∪ {3,5} = {1,3,5} (All elements of (A∩B) and the elements of (A∩C) which are not there in (A∩B)) (A∩B)∪(A∩C) = {1,3,5}
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