## Algebra 1

Published by Prentice Hall

# 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.

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