Question:
Which of the following is a singleton set?
Which of the following is a singleton set?
Updated On: Jul 7, 2022
- $\{x : |x| < 1, x \in I\}$
- $\{x: |x| = 5, x \in I\}$
- $\{x : x^2= 1, x \in I\}$
- $\{x: x^2 + x + 1 = 0, x \in R\}$
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The Correct Option is A
Solution and Explanation
(a) $\{x : |x| < 1,x \in I\}$
$ = \{x : -1 < x < 1, x \in I\} = \{0\}$
(b) $\{x : |x| = 5, x \in I\}$
$= \{x : x = ? 5\} = \{? 5\}$
(c) $\{x : x^2 = 1, x \in I\}$
$= \{x : x = ? 1\} = \{? 1\}$
(d) $\{x : x^2 + x + 1 = 0, x \in R\}$
$= \left\{x : x = \frac{-1\pm\sqrt{3}i}{2}, x \in R\right\} = \phi$
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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 "|".