Question:
Which of the following is not an empty set?
Which of the following is not an empty set?
Updated On: Jul 18, 2023
- Set of natural numbers $< 1$
- Natural number between $3$ and $4$
- The set of integers between $-2$ and $-3$
- The set $A = \{x: x^2 = 2 \,\forall \,x \,\in\, R\}$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
There is no natural number less than $1$
$\therefore\,$ Option $(a)$ is an empty set.
There is no natural number between $3$ and $4$
$\therefore\,$ Option $(b)$ is an empty set.
Between two consecutive integers, there exist no integer.
So option $(c)$ is an empty set.
Now, $x^{2} = 2\,\forall\,x \in R$
$\Rightarrow x = \pm\sqrt{2}$
$\therefore\, A = \left\{-\sqrt{2}, \sqrt{2}\right\}$, which contain elements.
$\therefore\,$ It is not an empty set.
Was this answer helpful?
1
0
Top Questions on Sets
- The distance of the point \( (2, 3) \) from the line \( 2x - 3y + 28 = 0 \), measured parallel to the line \( \sqrt{3}x - y + 1 = 0 \), is equal to
- Two finite sets have $ m $ and $ n $ number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $ m $ and $ n $ are respectively.
The shaded region in the Venn diagram represents
- Which of the following is a null set?
- Which of the following statement is true?
View More Questions
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 "|".