Pretty lost on this one...

For the set X = {m,n,q,p,r,s}, let R be the relation on P(x) (power set) given by A R B iff A and B have the same number of elements. List all the elements in {m}/R; in {m,n,q,p,r}/R. How many elements are in X/R? How many elements are in P(x)/R?

Any ideas?

4/15/2007 8:45:13 PM

I'm tired, so this might be wrong.

For starters, we know |P(x)| = 2^6 = 64.

for {m}/R, we only have two sets, null and {m}, both have a different number of elements, so they are both in {m}/R

for {m,n,q,p,r}/R, the only distinct sets are Null, {m}, {m,n}, {m,n,q}, {m,n,q,p}, and {m,n,q,p,r} since all other sets have the same number of elements as one of those sets.

For X/R, we only have the additional set {m,n,q,p,r,s}, so there are 7 total.

I tihnk.

4/15/2007 9:20:50 PM

never mind...

[Edited on April 15, 2007 at 11:58 PM. Reason : .]

4/15/2007 11:51:59 PM

im still confused on where the power set part totally comes into play

4/16/2007 12:00:07 AM

I'm not really sure either. I was hoping calias was going to answer.

4/16/2007 12:13:13 AM

Well you've got six elements, so the power set has what, 2^6 = 64 elements. Write them down and proceed from there.

4/16/2007 1:06:16 AM