Partition induced by a relation

Oct 2009
I'm not sure what you mean

{3} is in the powerset of B.

So it is in the partition described completely by

{3} 000
{3,6} 001
{3,5} 010
{3,5,6} 011
{3,4} 100
{3,4,6} 101
{3,4,5} 110
{3,4,5,6} 111

where I wrote binary numbers alongside to show how I was choosing elements from A that are not in B. So the above 8 sets all have the same intersection with B, so are equivalent under R, and there are no other sets in this partition.

Am I wrong?

No, re-reading your post you only gave 4 sets which are within one single equivalence class in \(\displaystyle P(A)\) , whereas I misunderstood and thought those were the eq. clases . As I warned, it was either you or me were wrong...and it was me. (Itwasntme)
Thanx for the explanation.