Course: Foundations of Higher Math

A relation is defined on byx R yif is even. Prove that is an equivalence relation. Determine the distinct equivalence classes.

Reflexivity:

Let .

which is even, sox R x.Symmetry:

Let .

Assume thatx R y,i.e. , .

which is even, soy R x.

Is this method fine?

Also, how would I notate the equivalence classes? I believe that there will be 2 distinct classes because 3x and 7y must have same parity for the difference to be even.

1.

2. ?