Question:
If $ S=\{(a,\,b):b=|a-1|,a\in Z $ and $ |a|<3\}, $ where $Z$ denotes the set of integers. Then, the range set of $S$ is
If $ S=\{(a,\,b):b=|a-1|,a\in Z $ and $ |a|<3\}, $ where $Z$ denotes the set of integers. Then, the range set of $S$ is
Updated On: Jun 23, 2024
- $ \{1,\,2,\,3\} $
- $ \{-1,\,2,\,3,\,1\} $
- $ \{0,\,1,\,2,\,3,\,4\} $
- $ \{-\,1,-\,2,-\,3,-\,4\} $
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The Correct Option is C
Solution and Explanation
Given, $ S=\{(a,\,b):b=|a-1|,\,a\,\in Z $
and $ |a| < 3\} $ $ z\to $ set of integers.
$ \therefore $ $ S=\{(-2,3),(-1,2),(0,1),(1,0),(2,1)\} $
$ \therefore $ Range of set $ (S)=\{0,1,2,3\} $
$ (\because \,|a|\, < 3\,\,\Rightarrow \,\,-3 < a < 3) $
and $ |a| < 3\} $ $ z\to $ set of integers.
$ \therefore $ $ S=\{(-2,3),(-1,2),(0,1),(1,0),(2,1)\} $
$ \therefore $ Range of set $ (S)=\{0,1,2,3\} $
$ (\because \,|a|\, < 3\,\,\Rightarrow \,\,-3 < a < 3) $
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Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
