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Question

Mathematics Question on Sets

If X=\left\\{-2, -1, 0, 1,2,3, 4, 5, 6, 7, 8\right\\} and A=\left\\{x : \left|x-2\right|\le3, x \, is\,an\, integer\right\\}, then X−A=X-A=

A

−2,6,7,8\\{-2, 6, 7, 8\\}

B

−2,−1,1,2,3,4,5,6\\{-2, -1, 1, 2, 3, 4, 5, 6\\}

C

−1,0,1,2,3,4,5,7,8\\{-1, 0,1,2,3, 4, 5, 7, 8\\}

D

−2,−1,2,3,6,7,8\\{-2, -1, 2, 3, 6, 7, 8\\}

Answer

−2,6,7,8\\{-2, 6, 7, 8\\}

Explanation

Solution

We have, X=−2,−1,0,1,8X = {-2, - 1 , 0 , 1 , 8 } and
A=x:∣x−2∣≤3,x is an integerA = {x : | x - 2| \le 3, x \text{ is an integer}}
∴A=−1,0,1,2,3,4,5\therefore A = {-1, 0, 1, 2, 3, 4, 5}
Now, X−A=−2,6,7,8X - A = {-2, 6, 7, 8}