1.
Venn diagram
a={ 1 2 3 4 }
b={ 2 3 4 5 6 }
2 5
6
1
4 3
Find a ∪ b
Find a ⋂ b
Find a ∪ b
1
2
3
4
Find a⋂b
Is adiagramthat help us visualizes the logical relationship between sets and elements

2.
Example: the set A containeven numbers from 1 to 25 and set B containthe multiple of 5 to 25
The interesting part shows that
A={ 2,4,6,8,10 ………24 }
B={ 5,10,15,20,25 }
a ∪ b ={ 10 , 20 }
4
2
8
6
12
14
16
18
22
24
10
20
5
15
25

3.
Q= from the shape given below answer the following :-
1) A ⋃ B = { 1,2,10,6,9}
2) A ⋂ B = {2}
3) A ⋂ B ⋂ C = {2}
4) 𝐴𝐶
= {6,9}
10
2
2
1
9
6
10
NOTE: 𝐴𝐶 is read as complement element that
don`t belong to set A

4.
Surveys:- people involving of people ( or other object ) same times require analyzing know in
formation a bout certain subset to obtaincardinalnumber of other subsets.
Example:- suppose that a group of 150 people were questions about particular social media media platform
that they used
90 Used Instagram
62 Used TikTok
38 Used Facebook
42 used Instagram and Tiktok
20 used Tiktok and Facebook
25 used Instagram and Facebook
18 used all there
How can we analyze this surey using venn diagram

5.
1 2
3
18
18 is for all
42= 18 + 24
20= 18 + 24
25= 18 + 7
18
24
7 2
41
24
18
7
18
11
2
41= 24 + 18 + 7 =
18= 24 + 18 + 2 =
11= 2 + 18 + 7 =

6.
Matrix:- what is the matrix ?
A matrix is a regtardar array of numbers arraged in rowsand colums it is usual to enclose the
arraign breackets
Example:-
2
7
-10
3.1
2
15
col2
col1
Row 1
Row 2
Row 3
M=
We say that a matrix is an MxN matrix or has sizeMxN
2*3

7.
Example:- M size equel ( 3*2 )
Remember that the first indexrefer to the row and the second indexto the column
A11
A21
A12……A1n
A22………
Am1……… Amn
Vectors:- A n*1 matrix that is matrix n rows and one column is called
column vector
1*n a={ 1 10 -2 4 }
b= 10
20
30
11

8.
Additionand subtraction of matnices add , and sub of matrix is done by addingor subtracting
corres ponding companents
Note : it can only be done where the matrix are the same size
Example:-
a= b=
7 2
-2
10
-2 -3
7 4
Find a+b
7 2
-2
10
-2 -3
7 4
+ =
5 -1
17 2

9.
Find a-b =
9 5
3 -6
Find b-a =
-9 -5
-3 6
2 7
-3 2
10 -5
4 11
1 0
1 0
a= b= c=
Find a+b+c =
13 2
2 13
Find a-b+c = for you
Find c-b+a = for you