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: 66


The total number of proper subsets is $31$.

Work Step by Step

The set of coins worth less than a dollar is: {penny, nickel, dime, quarter, half dollar} A set of $n$ elements has $2^n$ subsets. This set has 5 elements, therefore it has $2^5=32$ subsets. However, we are asked for distinct subsets; therefore we have to take 1 from the result, as one of the subsets is going to be the set itself. The total number of proper subsets is $32-1=31$.
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