Which of the following is an empty set?
- $\{ x | x$ is a real number and $x^2 - 1 = 0\}$
- $\{ x | x$ is a real number and $x^2 + 3 = 0\}$
- $\{ x | x$ is a real number and $x^2 - 9 = 0\}$
- $\{ x | x$ is a real number and $x^2= x +2\}$
The Correct Option is B
Solution and Explanation
$\Rightarrow \, x = \sqrt{-3} \in C$
$\Rightarrow \, x $ is not a real number
$ \therefore$ It is an empty set.
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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 "|".