SOLUTION: The number of subsets of a set with n elements is n^2 True or False?

False it's 2n.

That's because when constructing a subset of a given set,

There are 2 possible choices to make for the 1st element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2 choices for the first element of the given set in
taking a subset.
---
There are 2 possible choices to make for the 2nd element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2*2 or 22 choices for the first 2 elements 
of the given set in taking a subset from it.
---
There are 2 possible choices to make for the 3rd element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2*2*2 or 23 choices for the first 3 elements 
of the given set in taking a subset from it.
---
...
...
...
There are 2 possible choices to make for the nth element of
the set from which we are forming a subset.
1. Use it as an element of the subset we are making.
 or
2. Don't use it as as an element of the subset we are making.

That's 2*2*...*2 or 2n choices for the n element 
of the given set in taking a subset from it.

Edwin