Thread: Power Sets

I have a question here that says:

Let A = {1,2,3,4,5,6} and let S = P(A), the power set of A.

a) For a,b belong to S, define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence relation on S.

b) How many equivalence classes are there? List one element from each equivalence class.

Could someone steer me in the right direction? Thank you.

Originally Posted by GreenDay14

I have a question here that says:
Let A = {1,2,3,4,5,6} and let S = P(A), the power set of A.
a) For a,b belong to S, define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence relation on S.

b) How many equivalence classes are there? List one element from each equivalence class.

If from six we choose two, that can be done 15 ways.
So the are 15 two element subsets. Hence equivalence class of two element subsets has 15 members.

There are 7 different equivalence classes, one has only one element.