Thinking Mathematically (6th Edition)

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

Chapter 2 - Set Theory - 2.2 Subsets - Concept and Vocabulary Check - Page 67: 5


$2^{n}$ - 1.

Work Step by Step

The number of distinct proper subsets of a set with n elements is $2^{n}$ - 1. we know that every subset except the set itself is a proper subset. In Table 2.4, we included the set itself when counting the number of subsets. If we want to find the number of proper subsets, we must exclude counting the given set, thereby decreasing the number by 1.
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