Question
Tue April 08, 2014 By: Trisha Gupta

SIR I AM FACING DIFFICULTY IN FORMING VENN DIAGRAMS . CAN YOU HELP ME OUT . PLEASE DESCRIBE THE WAYS TO DO IT.

 

Expert Reply
Tue April 08, 2014
Venn diagrams are pictorial representations used to display mathematical or logical relationships between two or more given sets.
The drawing consists of two or more circles, each representing a specific group.
Each Venn diagram begins with a rectangle representing the universal set  U. 
Then each set in the problem is represented by a circle.
Any values that belong to more than one set will be placed in the sections where the circles overlap.
A typical venn diagram is shown in the figure below:


 
In the figure, set A contains the multiples of 2 which are less than 30 and set B contains multiples of 3 which are less than 25. Therefore, A = {2, 4, 6, 8, 10, 12... 26, 28} and B = {3, 6, 9, 12... 21, 24}. 
The various areas in the above diagram depict the following relationships: 

 1) Intersection (AintersectionB)- Denotes the set of elements that are shared by two or more given sets. In the figure
given below, the intersection of the two sets is shown.


   (AintersectionB) = {6, 12, 18, 24} 

2) Union (AUB)- Denotes all the elements of the given sets taken once.

A U B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28} 

Examples

1. From a survey of 100 college students, a marketing research company found that 75 students owned stereos, 45 owned cars, and 35 owned cars and stereos.
a) How many students owned either a car or a stereo?

b) How many students did not own either a car or a stereo?

 METHOD:

a) Start with a Venn Diagram and label the different categories:

b) Fill in the number of students who own both cars and stereos, which would be in the intersection of the two sets:

c) Fill in the remaining numbers for the two sets. In this case, since a total of 45 students own cars, and 35 have already been listed, then 45 - 35 = 10students own cars only. Similarly, since 75 students own stereos and 35 have already been listed, then 75 - 35 = 40 students who own stereos only:

d) Finally, interpret and answer the questions:



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