Hello all, first post here :-)

I'm not sure what all the proper English names are for this subject, so bear with me, please.

Given a set A = {1,2,3,4}

And set K = set of all equivalence relations of A.

Is {(1,1)(2,2)(3,3)(4,4)(1,2)(2,1)} an equivalence relation over A, and as such a member of K?

The question I need help with is : given these sets, if Ia is removed - what is the minimal member of K? Give two examples and prove that they are minimal.

I'm just starting this University math stuff and feeling very lost.

Thanks,

Emil.