A relation is an equivalence relation if and only if it has these three properties:

1)Reflexive: xRx for every x in the set.

x- x= 0 so that is easy

2)Symmetric: if xRy then yRx.

If xRy then either x- y is a multiple of n or x+ y is a multiple of n. For the first of those, you need the fact that y- x= -(x- y).

3)Transitive: if xRy and yRz then xRz.

If xRy then either x- y is a multiple of n or x+ y is a multiple of n. If yRz then either y- z is a multiple of n or y+ z is a multiple of n. You really need to look at 4 cases:

a) x- y is a multiple of n and y- z is a multiple of n. What is (x-y)+ (y- z)?

b) x- y is a multiple of n and y+ z is a multiple of n. What is (x-y)+ (y+ z)?

c) x+ y is a multiple of n and y- z is a multiple of n. What is (x+y)- (y- z)?

d) x+ y is a multiple of n and y+ z is a multiple of n. What is (x+y)- (y+z)?