Find all the partition class sets of Z = {1, 2, 3} of the equivalence relation A R B = A ∪ Y = Y ∪ B.

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We have partition class Z = {1, 2, 3}. And the task is to find all the sets of partition class of this equivalence R. And the relation is on the sets X = {1, 2, 3, 4, 5} and Y = {2, 4, 5} on the power set P(X).

So, I know that we have power set P(X) = {},{1},{2},{3},{4},{5},{1,2},{1,3},{1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5},{1,2,3},{1,2,4},{1,2,5},{1,3,4},{1,3,5},{1,4,5},{2,3,4},{2,3,5},{2,4,5},{3,4,5},{1,2,3,4},{1,2,3,5},{1,2,4,5},{1,3,4,5},{2,3,4,5},{1,2,3,4,5}.

But I'm bit stuck on how to process further with this question.

From what I can guess one of the sets would be {{1, 3} and {1, 2, 3}}.