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**MrJank** Give an example of an equivalence relation R on a set A = {1,2,3,4,5,6,7} with P the set of equivalence classes such that the following four properties are satisfied:

1. |P|=3

2. There exists no set S in P such that |S|=3

3. 3 R 4 but 3 R 5

4. there exists a set T in P such that 1, 7 in T

So far the only relations elements in the relation I can think of is:

R = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7), (3,5), (5,3), (1,7), (7,1)}

I'm not sure how to get the rest... I seem to be missing a key part of how I am supposed to do this.