Let A = {1,2,4,5,6,8,11,13,15,17,153}. Define a relation R on A by writing (x,y) $\displaystyle \epsilon$ R iff x - y is a multiple of 5.

a) Show that R is an equivalence on A.

My answer:

Is it reflexive? Yes, since x-x = $\displaystyle 5 \cdot 0$, $\displaystyle 0 \epsilon \mathbb{Z}$

Is it symmetric? No, since $\displaystyle x-y = 5k$ but $\displaystyle y-x = -5k$, $\displaystyle k \epsilon \mathbb{Z}$

Is this reflexive and symmetric ones correct? thanks