Thread: 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) 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 = ,
Is it symmetric? No, since but ,

Is this reflexive and symmetric ones correct? thanks

Originally Posted by jvignacio

Is it symmetric? No, since but ,

-5k=5(-k) and k is integer. (In other words, -5k is a multiple of 5, too.)
So it is reflexive.

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.