Question

prove that the equivalence relation defined in a set of rings is an equivalence relation

Answer 1

Answer:

To prove an equivalence relation, you must show reflexivity, symmetry, and transitivity, so using our example above, we can say:

Reflexivity: Since a – a = 0 and 0 is an integer, this shows that (a, a) is in the relation; thus, proving R is reflexive.

Symmetry: If a – b is an integer, then b – a is also an integer.