Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - 3-5 Working with Sets - Practice and Problem-Solving Exercises - Page 199: 50

Answer

If a set has x members, the number of subsets is $2^x$.

Work Step by Step

A null set has only 1 subset, the null set itself. A set with 1 member has twice that many subsets (2), including the null subset and the set itself. Look at the following example. Each time a member is added to the set, the number of subsets doubles. The subsets include all the subsets of the smaller set, plus a copy of those subsets with the new member added to each. { } : { } {1} : { }, {1} {1,2} : { }, {1}, {2}, {1,2} {1,2,3} : { }, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3} A set with 0 members has $2^0=1$ subsets. A set with 1 member has $2^1=2$ subsets. A set with 2 members has $2^2=4$ subsets. A set with 3 members has $2^3=8$ subsets. A set with 6 members has $2^6=64$ subsets., etc. Since the number of subsets doubles, the number of subsets can be expressed as a power of 2, where the exponent is the number of members in the set.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.