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Mathematics Question on Relations and functions

If S=\\{(a,\,b):b=|a-1|,a\in Z and |a|<3\\}, where ZZ denotes the set of integers. Then, the range set of SS is

A

1, 2, 3\\{1,\,2,\,3\\}

B

−1, 2, 3, 1\\{-1,\,2,\,3,\,1\\}

C

0, 1, 2, 3, 4\\{0,\,1,\,2,\,3,\,4\\}

D

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

Answer

0, 1, 2, 3, 4\\{0,\,1,\,2,\,3,\,4\\}

Explanation

Solution

Given, S=\\{(a,\,b):b=|a-1|,\,a\,\in Z
and |a| < 3\\} z→z\to set of integers.
∴\therefore S=(−2,3),(−1,2),(0,1),(1,0),(2,1)S=\\{(-2,3),(-1,2),(0,1),(1,0),(2,1)\\}
∴\therefore Range of set (S)=0,1,2,3(S)=\\{0,1,2,3\\}
(∵ ∣a∣ <3  ⇒  −3<a<3)(\because \,|a|\, < 3\,\,\Rightarrow \,\,-3 < a < 3)