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.
Thanks alot, that helps already!
The question has two parts.
In the first part, A is just an abstract set and K is the set of all its equivalence relations (of A);
The question is to prove that there is in fact a "smallest" member and a "largest" member in K. I gave the answer that the diagonal is the smallest because it is the smallest equivalence relation, and that AxA is the largest.
Hope that's true.
In the second part they say that A equals {1,2,3,4} and that K is again the set of equivalence relations, only i'm asked to remove the smallest and largest members that were found in part 1.
So the diagonal isn't a member of K now.
The question is to give an example of a "minimal" member and prove that it is in fact minimal.
Again, maybe you guys don't call it minimal and smallest, but I hope you can understand what I'm asking.
Thanks!