1. ## relations help (3)

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

a) Show that R is an equivalence on A.

Is it reflexive? Yes, since x-x = $5 \cdot 0$, $0 \epsilon \mathbb{Z}$
Is it symmetric? No, since $x-y = 5k$ but $y-x = -5k$, $k \epsilon \mathbb{Z}$

Is this reflexive and symmetric ones correct? thanks

2. Originally Posted by jvignacio
Is it symmetric? No, since $x-y = 5k$ but $y-x = -5k$, $k \epsilon \mathbb{Z}$
-5k=5(-k) and k is integer. (In other words, -5k is a multiple of 5, too.)
So it is reflexive.

3. Originally Posted by kompik
-5k=5(-k) and k is integer. (In other words, -5k is a multiple of 5, too.)
So it is reflexive.
Yep thats right forgot integers are minus numbers aswell.