Thinking Mathematically (6th Edition)

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

Chapter 2 - Set Theory - 2.2 Subsets - Exercise Set 2.2: 65

Answer

Total number of proper subsets are = 127

Work Step by Step

{X|X is a day of a week} = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} A set of n elements have 2^{n} number of subsets. Here set has 7 elements. So total number of subsets are 2^{7}=128. As these 128 subsets also include the one subset which is the set itself. We need to exclude this one subset. Thus Total number of proper subsets are = 128 - 1 = 127.
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