# 2 sets A= {x belongs to Z, with property 3/(x-2) belongs to Z} B = { x belongs to Z, with property (x-2)/3 belongs to Z} Find A, B, A-B

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### 1 Answer

In order to find A elements, we have to follow the property of the set.

The ratio 3/(x-2) belongs to Z, only if the result of division is exact. For that, the denominator must be a a divisor of 3, which means (x-2)=1, or (x-2)=-1, or (x-2)=3, or (x-2)=-3

x-2=1

x=2 +1=3

x-2=-1

x=2-1=1

x-2=3

x=2+3=5

x-2=-3

x=2-3

x=-1

A={-1,1,3,5}

In order to find B elements, we have to follow the property of the set.

(x-2) has to be a multiplex of 3, so that the ratio to be a whole number.

x-2 = 3k

x=2+3k

Now plug in values for k, in order to find out x values.

k=-3

x=2 + 3*(-3)=2 -9=-7

k=-2

x= 2 + 3*(-2)= 2 -6=-4

k=-1

x=2 + 3*(-1)=2-3=-1

k=0

x=2 + 3*(0)=2

k=1

x=2 + 3*(1)=2+3=5

B={.....-7,-4,-1,2,5,....,2+3k}

A-B=what elements are in A set and are not in B set= {1,3}