- #1

Yankel

- 395

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I have a few questions related to the different number of equivalence classes under some constraint. I don't know how to approach them, if you could guide me to it, maybe if I do a few I can do the others. Thank you.

Given the set A={1,2,3,4,5},

1) How many different equivalence relations are there on A, with two equivalence classes?

2) How many different equivalence relations are there on A, with no three equivalence classes (other number rather than 3)?

3) How many different equivalence relations are there on A, which includes the pair (1,3) ?

4) How many different equivalence relations are there on A, with three equivalence classes?

I do not know how to approach this kind of questions. Can you please assist and give me some guidance ?

Thank you in advance.