What Is the Power Set of the Empty Set?

[jaqueh]

Homework Statement

Is this true or false

Homework Equations

{{ø}} is a subset of P({ø,{ø}})

The Attempt at a Solution

I'm thinking that it is since to make the subset {ø} into a power set it becomes {{ø}}?

 

[HallsofIvy]

I'm curious as to why you titled this "power set of the empty set" since none of the sets mentioned are empty.

Yes, {ø, {ø}} has two members and so has four subsets: {}, {ø}, {{ø}} and {ø,{ø}}