Recall that 3/k if and only if there exist nEz at k=3n. Let a and b be integers.

Define (equal sign with three bars and subscript 3) as a(equal sign with three bars and subscript 3) b if and only if 3/(a-b)

Prove the fallowing

1) for every int a, a(equal sign with three bars and subscript 3)a

2) for every in a, b if a(equal sign with three bars and subscript 3)b then b must be the same with a

3) for every int a, b, c if a(equal sign with three bars and subscript 3)b b(equal sign with three bars and subscript 3)c a(equal sign with three bars and subscript 3)c