If we have two sets A = { x belongs to Z, with property 3/(x-2) belongs to ZB = {x belongs to Z , with property ( x-2)/3 belongs to Z . Find A,...

x is an element of A  where x belongs to z

That means that x should be an integer (1,2,3...)

We have 3/(x-2) is an integer , then (x-3) should be divided by 3.

Then (x-2) should be either 3,-3, 1, or -1

x-2=3 ==> x=5

x-3=-3 ==> x=0

x-2=1 ==> x=3

x-2=-1==> x=1

Then A elements are 0,1,3, 5

A= {0,1,3,5}

Now for B. B elements should verify (x-2)/3

Since x belongs top z, then x-2)/3 should be an integer, that means (x-2) is a multiplex of 3

(x-2)= 3n where  n=...-3,-2,-2,1,0,1,2,3....

x-2= 3(-2) ==> X=-4

X-2=3(-1) ==> X=-1

x-2= 3(0) ==> x=2

x-2=3(1) ==> x= 5

x-2=3(2) ==> x=8

x-2=3(3) ==> x= 11

==> B = {...-4,-1,2,5,8,11,...}

Then A-B elements are all elements in A without elements in B:

A-B = A - (A intersect B)

A-B    =  {0,1,3,5}-{5} = {0,1,3}