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

Let [0]={xEz: 0 (equal sign with three bars and subscript 3) x}

[1]={xEz: 1(equal sign with three bars and subscript 3)x}

[2]={xEz: 2(equal sign with three bars and subscript 3)x}

Part B is

Show that the sets [0] [1] [2] partition Z