Set word problem1





 In this page set word problem1 we will see the problem and how to solve the problem. Using the same method students can try to solve the given practice problem.

Question:

There are 40 students in a class. 20 take Chemistry and 25 take French. 8 students take both.

  1. Find how many students take none.
  2. How many are there in at least one classes?

Solution:

We will solve the problem using venn diagram. First let us write all the given information.

         Universal set U              =    40

    Students take Chemistry C   =    20

    Students take French    F    =    25

    Students take both CnF       =     8

 

Now let us enter the information in venn diagram. Here we have universal set. So we have to draw a rectangle to represent the universal set. There are two classification C and F. For that let us draw two overlapping circles.


As there are 8 students who are taking both let us enter 8 in the overlapping area of the circles C and F.


There are 20 students who take chemistry, but we had already entered 8 students. So we have to enter only 12(20-8=12) in chemistry only area.


Now in French there are 25 students, but we have already entered 8 students. So we have to enter only 17(25-8=17) in French only area.


That gives the total number of students who have taken either Chemistry or French classes.

12+8+17= 37. The number of students who had taken none is

40-37 = 3

From the final venn diagram we can get the answers for our questions.

  1. Find how many students take none.
  2. How many are there in at least one classes?

The answers are :

  1. The number of students who had taken none is 3
  2. There are 37 students in at least one class.

Practice problem:

A group of 20 college students were asked whether they are using the social net working sites. For that 8 said they use face book. 10 said they use twitter. 4 said they use both.

  1. Find how many are not using none?
  2. Find how many are using only face book and twitter?




                                  Set word problems

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