Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 12 - Counting and Probability - Section 12.1 Counting - 12.1 Assess Your Understanding - Page 867: 9

Answer

The $16$ subsets are: $\{\}, \{a\},\{b\},\{c\},\{d\}, \{a,b\},\{a,c\},\{a,d\},\\ \{b,c\},\{b,d\},\{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\}, \text{ and }\{a,b,c,d\}$.

Work Step by Step

The subsets with no elements are: $\{\}$. The subsets with $1$ element are: $\{a\},\{b\},\{c\},\{d\},$. The subsets with $2$ elements are: $\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}$. The subsets with $3$ elements are: $\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\}$. The subsets with $4$ elements are: $\{a,b,c,d\}$. Thus there are $16$ subsets.
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