Homework Help: Power Sets

1. Nov 17, 2012

nicnicman

While practicing power set problems I came across one that has me stumped.

The problem asks: Is the following set is a power set of of a set?
{∅, {b, ∅}, {a}, {a, b}, {b}}

My answer: This set has 5 elements. Since 5 is not a power of 2, this cannot be the power set of any set.

The problem then asks: If the set is not a power set of a set, then what is the lacking set?

This is where I'm stuck. There are no similar problems in the book or on the Internet (that I can find), and I'm not sure how to answer this.

Thank you for any suggestions!

2. Nov 17, 2012

SammyS

Staff Emeritus
If these are elements of the power set of some set, S, start my making a list of the elements of set S.

3. Nov 17, 2012

nicnicman

Okay if S = {∅, a, b},
then P(S) = [{∅, {∅}, {a}, {b}, {∅, a}, {∅, b}, {a, b}, {∅, a, b}]
Thus, the missing sets are {∅}, {∅, a}, and {∅, a, b}.

Is this correct?

Last edited: Nov 18, 2012
4. Nov 18, 2012

SammyS

Staff Emeritus
Yes.

5. Nov 18, 2012

nicnicman

Great! Thanks for the help.