Home
Arithmetic
Algebra
Geometry
Statistics
Probability
Set Theory
Trigonometry
Matrices
Vectors
Calculus
SAT Preparation
ACT Preparation
GMAT Preparation
Interactive Zone
Math Worksheets
Math Games
Fun Games
Math Trivia
English Help
Chemistry
Animal Facts
Tutoring Services
What's New
Links

 

Sets Intersection: Intersection Of Three Sets

 

 

The intersection of three sets X, Y and Z is the set of elements that are common to sets X, Y and Z. It is denoted by XYZ


Example:

Draw a Venn diagram to represent the relationship between the sets

X = {1, 2, 5, 6, 7, 9}, Y = {1, 3, 4, 5, 6, 8} and

Z = {3, 5, 6, 7, 8, 10}

Solution:

We find that XYZ = {5, 6}, X Y = {1, 5, 6},

YZ = {3, 5, 6, 8} and XZ = {5, 6, 7}

For the Venn diagram:

Step 1 : Draw three overlapping circles to represent the three sets.

Step 2 : Write down the elements in the intersection XYZ

Step 3 : Write down the remaining elements in the intersections:

XY, YZ and XZ

Step 4 : Write down the remaining elements in the respective sets.

Again, notice that you start filling the Venn diagram from the elements in the intersection first.

 

 

In general, there are many ways that 3 sets may intersect. Some examples are shown below.


 

 

Videos

Sets, Intersections, and Unions -
Professor Edward Burger explains sets, intersections, and unions.

 

The following video describes the Union and Intersection of Sets

 

 

 

Custom Search

 

We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.

 

© Copyright 2005, 2008 - onlinemathlearning.com
Embedded content, if any, are copyrights of their respective owners.

Useful Links:
Sets
 

 

 

Custom Search