Venn Diagram

published by SWOT

Introduction

In this article of set theory,we are going to solve a problem on Venn diagram (So sorry,image preview for Venn Diagram not available yet,but don't worry,you will understand it without the diagram). So, let's go over to problem of today:

 • In a recent survey of 400 students in a school,100 are listed as smokers and 150 as Chewers of gum,75 were listed as both smokers and Chewers of gum. Find out how many students are neither smokers nor Chewers of gum. (get a rough paper to solve as you study)

SOLUTION:

U = universal set = number of students,

Let S = Smokers

       C = Chewers of gum

       N = students that are neither S nor C

Then S = 100 , C = 150 , S intersection C = 75 , N = ?.

Since the total number of students who are smokers ONLY is the number of students who are smokers Minos number of students who are smokers and also a chewer of gum. That is:

S = n(S) - n(S п C),

 = 100 - 75,

S = 25

and 

Since the total number of students who are Chewers of gum ONLY is the number of students who are Chewers of gum Minos number of students who are Chewers of gum and also a smoker. That is:

C = n(C) - n(C п S),

 = 150 - 75,

C = 75

Therefore,the number of students that are neither smokers nor Chewers of gum is:

n(S ц C) = n(U) - N,

 make N subject of the formula,

N = n(U) - n(S ц C)

N = 400 - (25 + 75 + 75)

N = 400 - 175

N = 225

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