CBSE Class 11-science Answered

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

Asked by Trisha Gupta | 08 Apr, 2014, 04:39: PM

Expert Answer

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 (AB)- 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.

(AB) = {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: