1. ## Isomorphism

If A' is isomorphic to A'' and B' is isomorphic to B'' then A'UB' is isomorphic to A''UB''. (their intersections are empty).
Moreover conclude that the disjoint union is well-defined up to isomorphism.

2. ## Re: Isomorphism

Hey jcir2826.

Can you use results about equivalence classes and partitions for this result? (i.e. show that disjoint equivalence classes have a natural extension to isomorphism results)

3. ## Re: Isomorphism

The would help for the second part.

4. ## Re: Isomorphism

Originally Posted by jcir2826
If A' is isomorphic to A'' and B' is isomorphic to B'' then A'UB' is isomorphic to A''UB''. (their intersections are empty).
I assume this means A' ∩ B' = ∅ and A'' ∩ B'' = ∅. And what are A', B', A'' and B'': sets, groups, rings, or something else?

5. ## Re: Isomorphism

They are sets. the assumption is correct.