EMPTY SET

Empty Set

Definition Of Empty Set

An Empty Set is a set with no elements. It can be symbolized by {} or ø

The solution set for an equation that has no solution is also called an empty set.It is also called a null set.

Video Examples: The Empty Set or the Null Set , Intermediate Algebra

Example of Empty Set

A = {2, 6, 8} and B = {3, 5, 7}
Let C represent the intersection of the sets A and B.
C = {}, a null set, because there is no element common between the two sets.

Solved Example on Empty Set

Ques: Solve |6x - 7| + 10 = 0.

Choices:

A. ø
B. - 10
C. - 1/2
D. {- 1/2, 17/6}
Correct Answer: A

Solution:

Step 1: |6x - 7| + 10 = 0
Step 2: |6x - 7| = - 10, which is never true. [Subtract 10 from each side.]
Step 3: So, the solution set is {} or a null set ø.

Quick Summary

A set containing no elements.
Represented by {} or ø.
Also called a null set.

\[ \{\} \text{ or } \emptyset \]

🍎 Teacher Insights

Emphasize that the empty set is not the same as zero. Use visual aids to show sets with and without elements.

🎓 Prerequisites

Set
Element

Check Your Knowledge

Q1: Which of the following represents an empty set?

{0} { } {1, 2} {a, b, c}

Q2: The intersection of A = {1, 2} and B = {3, 4} is:

{1, 2, 3, 4} {1} { } {3}

Frequently Asked Questions

Q: Is the empty set a subset of every set?
A: Yes, the empty set is a subset of every set.

Q: Is the empty set equal to zero?
A: No, the empty set is a set, while zero is a number. They are different mathematical objects.