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: 96

Answer

The dispatcher has 16 options for sending the cars.

Work Step by Step

We could represent the set of cars using the roster method: {Car #1, Car #2, Car #3, Car #4} Since the dispatcher can send none, one, two, three, or all four cars, the number of options is going to be equal to the number of subsets of the given set. A set of $n$ elements has $2^n$ subsets; therefore, our set has: $2^4=16$ subsets. The dispatcher has 16 options for sending the cars.
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