Question:
Write the set builder form $A = {-1, 1}$
Write the set builder form $A = {-1, 1}$
Updated On: Sep 4, 2024
- A = {x : x is a real number}
- A = (x : x is an integer)
- A = {x : x is a root of the equation $x^2$ = 1}
- A = {x : x is a root of the equation $x^2$ + 1 = 0}
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The Correct Option is C
Solution and Explanation
$-1,1$ are the roots of the equation $x^{2}-1=0$ Hence, set builder form of $A$ can be written as $A=\left\{x: x\right.$ is a root of the equation $\left.x^{2}=1\right\}$
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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 "|".