** **

The study of sets helps in increasing the degree of relations in such a way that it optimizes the bond

between any two ,three or many quantities taken together.

Set: A well-defined collection of objects is defined as a set.

Example: Set of vowels A= {a, e, i, o, u}

**Note: **
All the sets are denoted by capital letters

Symbols used in sets:

Union: U

Intersection: ∩

Subset: C

** **

If there are two sets given say A and B then the common data found in these two sets is called common data set.

Example A= {a, e, i, o, u} B= {a, i, o}

Then we find the common data set between t**hese two sets namely A ∩ B = {a, i, o}.**

** **

** **

** **
The joining of two set elements together is called union of sets

Example: A= {2, 5, 7} B= {a, g, h}

** AUB**
= {a, g, h, 2, 5, 7}

**Example **
A= {1, 5} B= {5}

Then we find the common data set between t**hese two sets namely A ∩ B = {5}.**

** **

** **
What is a cardinal number? The number of elements in the given set is called a cardinal number.

Example: A= {1, 2, a, v}

In the above example there are 4 elements in the given set.

Hence we define cardinal number as 4.

** **

**Sets Solved Problems**

** **

Given A= {1, 2} B= {6, 3}

Find

1. A ∩ B

2. AUB

3. Cardinal number of A and B

If A= {2, 6, 7, 8} B= {2, 6, 3} find A ∩ B

A ∩ B = {2, 6}, so the common elements are shaded in yellow.

In a total of 30 players , 25 play hockey and 10 play Rugby can you predict using set theory that how players are liking to play both.

The formulae is n *(*A U B*)* = n *(*A*)* + n *(*B*)* - n *(*A ∩ B*)*

Here n *(*A U B*)* = cardinal number of both set A and set B *(*hockey and rugby*)*

n *(*A*)*= cardinal number of only set A *(*Hockey only*)*

n *(*B*)* = cardinal number of only set B *(*Rugby*)*.

And

n *(*A ∩ B*)* = cardinal number for both hockey and rugby

30 = 25 +10 - n *(*A ∩ B*)* so transfer n *(*A ∩ B*)* towards left side we get

n *(*A ∩ B*)* = 35-30

= 5

So the number of players who play both is 5.

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