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.

Examples 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

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.                         

Related Terms for Empty Set

  • Set
  • Element
  • Solution set
  • Equation