# relations help (3)

• Apr 18th 2010, 04:22 AM
jvignacio
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) $\displaystyle \epsilon$ 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 = $\displaystyle 5 \cdot 0$, $\displaystyle 0 \epsilon \mathbb{Z}$
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
• Apr 18th 2010, 04:37 AM
kompik
Quote:

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

-5k=5(-k) and k is integer. (In other words, -5k is a multiple of 5, too.)
So it is reflexive.
• Apr 18th 2010, 04:49 AM
jvignacio
Quote:

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.