If N7 = {1,2,3,4,5,6,7}, does the following partitions give rise to an equivalence relation? Why?
A1={1,2,5,7}, A2={3}, A3={4,6}.

Dear student
Your questions seems incompete. A relation R on set A is a subset of A X A. However I am assuming that you are talking about universal relations on set A1, A2, and A3; i.e. whole set of A1 X A1, A2  X A2 and A3 X A3.





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