Principle of inclusion and exclusion for two sets with examples

1. Principal Of Inclusion
& Exclusion
By Vishal Maher
1

2. Welcome To This Tutorial,
In This Tutorial We Will Be Discuss
About Principal Of Inclusion &
Exclusion
2

3. Cardinality Of Set
3

4. Cardinality Of Set
 Number of elements present in a set
A = {a, b, c, d, e}
|A|= 5
 And it is denoted by |A|
4

5. Operations On Two Set
|A∪B| = |A| + |B| - |A∩B|
5

6. Ex.
Let A={a, b, c, d, e} and
B={c, e, f, h, k, m} find |A∪B| using Inclusion & Exclusion
Principle of two set
A∪B={a, b, c, d, e, f, h, k, m}
|A ∪B|=9
A ∩B={c, e}
|A ∩B|=2
|A|=5
|B|=6
|A ∪B|=|A|+|B|-|A ∩B|
9=5+6-2
9=11-2
9=9
This Is The Proof Of This Principle
6

7. Ex.
A company want to hire 25 programmers to handle system programing job & 40 Programmers
for application program, of those hire 10 will be expected to perform job of both types. How
many programmer be hire by the company?
Let A is set of system Programmers & B is set of application programmers
|A|=25
|B|=40
|A ∩B|=10
|A ∪B| =|A|+|B|-|A ∩B|
=25+40-10
=65-10
|A ∪B| =55
 55 Programmers are to be hired by the company
7

8. Thank You
8