Cartesian Products Of Sets
Chapter Name : Relations And Functions |
Sub Topic Code : 104_11_02_02_01 |
Topic Name : Cartesian Products Of Sets |
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Sub Topic Name : Cartesian Products Of Sets |
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Introduction
A set containing all possible combinations whose first element is from set 1 and the other element is from set 2 is known as the Cartesian product of the sets.
Pre-Requisites:
What are relations and functions?
Activity:
How many number of different meals from a given number of different items like meats, salads, vegetables, and drinks can be supplied?
Real Life Question:
How many pairs of bag, shirt and coat can be formed of blue and red colour?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Cartesian Product | The Cartesian product P X Q is the set of all ordered pairs of elements from two given non empty sets P and Q. P X Q = { (p,q) : p ? P, q ? Q } |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Take 3 different coloured bins and 10 different colored balls. Count the number of ways the balls can be put in each differently. | It would make the idea of a Cartesian product clearer. The bins represent one set and the balls represent the other. |
Real life uses :
The Cartesian product can be used to graph mathematical properties, as in Graphing equivalence and Graphing the total product.
Places to visit :
Math Lab.
Practical examples around us
| Examples | Explainations |
|---|---|
| 1. Calendar. | Weeks as one set (Rows) and weekdays (Columns) as another set, a set with a particular week and weekday gives the date (cell resulting due to the intersection of a particular row with a particular column). |
What you learn in Theory:
What is the cartesian product of two sets? What are ordered pairs?
What you learn in Practice:
How to find cartesian products of two sets and its use.