Cartesian Product of Two Sets

If A and B are two non-empty sets, then their Cartesian product A × B is the set of all ordered pair of elements from A and B.

        A × B = {(x, y) : x ∈ A, y ∈ B}

Suppose, if A and B are two non-empty sets, then the Cartesian product of two sets, A and set B is the set of all ordered pairs (a, b) such that a ∈A and b∈B which is denoted as A × B.

For Example; 

1. If A = {7, 8} and B = {2, 4, 6}, find A × B. 

Solution:

A × B = {(7, 2); (7, 4); (7, 6); (8, 2); (8, 4); (8, 6)} 

The 6 ordered pairs thus formed can represent the position of points in a plane, if a and B are subsets of a set of real numbers. 

2. If A × B = {(p, x); (p, y); (q, x); (q, y)}, find A and B. 

Solution:

A is a set of all first entries in ordered pairs in A × B.

B is a set of all second entries in ordered pairs in A × B.

Thus A = {p, q} and B = {x, y}


3. If A and B are two sets, and A × B consists of 6 elements: If three elements of A × B are (2, 5) (3, 7) (4, 7) find A × B.

Solution:

Since, (2, 5) (3, 7) and (4, 7) are elements of A × B.

So, we can say that 2, 3, 4 are the elements of A and 5, 7 are the elements of B.

So, A = {2, 3, 4} and B = {5, 7}

Now, A × B = {(2, 5); (2, 7); (3, 5); (3, 7); (4, 5); (4, 7)}

Thus, A × B contain six ordered pairs.


4. If A = { 1, 3, 5} and B = {2, 3}, then

Find: (i) A × B (ii) B × A (iii) A × A (iv) (B × B)

Solution:

A ×B={1, 3, 5} × {2,3} = [{1, 2},{1, 3},{3, 2},{3, 3},{5, 2},{5, 3}]

B × A = {2, 3} × {1, 3, 5} = [{2, 1},{2, 3},{2, 5},{3, 1},{3, 3},{3, 5}]

A × A = {1, 3, 5} × {1, 3, 5}= [{1, 1},{1, 3},{1, 5},{3, 1},{3, 3},{3, 5},{5, 1},{5, 3},{5, 5}]

B × B = {2, 3} × {2, 3} = [{2, 2},{2, 3},{3, 2},{3, 3}]

Note:

If either A or B are null sets, then A ×B will also be an empty set, i.e., if A = ∅ or

B = ∅, then A × B = ∅


 Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Relation

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function


 Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping











7th Grade Math Problems

8th Grade Math Practice

From Cartesian Product of Two Sets to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 01, 23 01:16 AM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  2. Days of the Week | 7 Days of the Week | What are the Seven Days?

    Nov 30, 23 10:59 PM

    Days of the Weeks
    We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…

    Read More

  3. Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical

    Nov 30, 23 01:08 PM

    Types of Lines
    What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…

    Read More