An equivalence relation

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Question from Francesca, a student:

In this problem we are told to find out if the given set is an equivalence relation or not.
{(x,y) such that 4 divides x-y}. What I am confused about is whether or not for instance if I picked (1,5) as a part of the set whether I could put in (5,1) as well or whether that would be wrong. Thanks!

Francesca,

Let's use another number instead of 4. Suppose R = {(a,b): 3 divides a-b}. Then (4, 1) is in R because 4 divides 4-1 = 3. Is (1, 4) in R? For that to be true, 3 would have to divide 1-4 = (-3). It does, since 3x(-1) = (-3). Therefore (1, 4) is in R to.

Good luck,
Victoria

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