We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

In this section, we will go through some practical problems on intersection of three sets.For solving such a problems we have to consider the following rules :

If A, B and C are three finite sets then :

1) n ( A ∪ B ∪ C ) =

n(A) + n(B) + n(C) – n ( A ∩ B ) – n(B ∩ C) – n (A ∩ C) + n( A ∩ B ∩ C )

2) n[ A ∩ ( B ∪ C) ] = n ( A ∩ B ) + n ( A ∩ C) – n( A ∩ B ∩ C)

1) In a survey of 200 students of a school it was found that 120 study mathematics, 90 study physics and 70 study chemistry, 40 study mathematics and physics, 30 study physics and chemistry, 50 study chemistry and mathematics and 20 study none of these subjects. Find the number of students who study all three subjects.

M = Mathematics ; P = Physics and C = Chemistry

n(M) = 120 n(P) = 90 n (C) = 70 n ( M ∩ P) = 40

n ( P ∩ C ) = 30 n ( C ∩ M ) = 50 n ( M ∪ P ∪ C )’ = 20

Now n(M ∪ P ∪ C)’ = n(U) – n(M ∪ P ∪ C)

20 = 200 – n (M ∪ P ∪ C)

Therefore, n(M ∪ P ∪ C) = 200 – 20 = 180

n(M ∪ P ∪ C)

= n(M) + n(P) + n(C) – n(M ∩ P) – n(P ∩ C) – n(C ∩ M) + n(M ∩ P ∩ C)

180 = 120 + 90 + 70 - 40 - 30 - 50 + n(M ∩ P ∩ C)

⇒ n(M ∩ P ∩ C) =180 - 120 - 90 - 70 + 40 + 30 + 50

⇒ n(M ∩ P ∩ C) = 20.

2) In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find the number of people who read at least one of the newspapers.(problems on intersection of three sets)

H = People who read newspaper H.

I = People who read newspaper I.

T = People who read newspaper T.

n(H) = 25 ; n(T)= 26 ; n(I)= 26 ; n(H ∩ I) = 9

n(H ∩ T) = 11 ; n(T ∩ I) = 8 and n(H ∩ T ∩ I) = 3

n(H ∪T ∪ I )= Number of people who read at least one of the newspapers

= n(H) + n(T) + n(I) – n(H ∩ T) – n(T ∩ I) – n(H ∩ I) + n(H ∩ T ∩ I)

n(H ∪T ∪ I )= 25+ 26 + 26 - 11 - 9 - 8 + 3

= 77 - 28 + 3

= 80 - 28

= 52

Hence the number of people who read at least one of the newspapers is 52.

• Sets

• Representation of Set

• Cardinal Number

• Types of Sets

• Pairs of Sets

• Subset

• Complement of Set

• Union of the Sets

• Intersection of Sets

• Operations on Sets

• De Morgan's Law

• Venn Diagrams

• Venn-diagrams for sets

• Venn-diagrams for different situations

• Problems on Intersection of Two Sets

• Problems on Intersection of Three Sets

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers