Question:
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= $
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= $
Updated On: Jul 22, 2024
- $ \{-2, 6, 7, 8\} $
- $ \{-2, -1, 1, 2, 3, 4, 5, 6\} $
- $ \{-1, 0,1,2,3, 4, 5, 7, 8\} $
- $\{-2, -1, 2, 3, 6, 7, 8\} $
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The Correct Option is A
Solution and Explanation
We have, $X = {-2, - 1 , 0 , 1 , 8 }$ and
$A = {x : | x - 2| \le 3, x \text{ is an integer}}$
$\therefore A = {-1, 0, 1, 2, 3, 4, 5}$
Now, $X - A = {-2, 6, 7, 8}$
$A = {x : | x - 2| \le 3, x \text{ is an integer}}$
$\therefore A = {-1, 0, 1, 2, 3, 4, 5}$
Now, $X - A = {-2, 6, 7, 8}$
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".