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