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**jvignacio** Hey guys, question... Let A = {1,2,3,4,5,6,7,8,9,10}. Define a relation R on A by writing (x,y) $\displaystyle \epsilon$ R iff 3|(x-y).

a) show that R is an equivalence relation on A.

**My answer:**

Is it reflexive? **Yes!** since x-x = 0 and 0 is divisible by 3. (Eg x = 6)

Is it symmetric? **Yes!** since if x-y is divisible by 3, then y-x is divisible by 3. (Eg, x=8, y=2)

Is it transitive? **Yes!** since if 3|(x-y) and 3|(y-z), then 3|(x-z). (Eg. x=10, y=1 and z=4).

Is this correct? thanks..