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- 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