Question

Among 130 students 60 study Math 51 study Physics and 30 studies both Math and Physics. Out of 54 students studying Chemistry, 26 study Math and Chemistry 21 study physics and Chemistry 12 study Math, Physics and Chemistry. All the students studying neither Math nor Physics are studying Biology. Find:- i) How many are studying Biology? ii) How many are not studying Chemistry are studying Math but no Physics? iii) How many are studying neither Math nor Physics nor Chemistry?

(Please write the appropriate answers.)

Answer 1

Answer:

this is answer for part i

Answer 2

1) There are 30 students studying biology

2) There are 28 Students studying math alone

3) There are 30 students studying neither math nor physics nor chemistry

Step-by-step explanation:

Given data

Total number of students n(T) = 130

students studying math n(M) = 60

Students studying Physics n(P) =51

Students studying Math and Physics (M∩P) = 30

Students studying Chemistry n(C) = 54

Students studying Math and Chemistry n(M∩C) =26

Students studying Physics and Chemistry n(P∩C) = 21

Students studying Math Physics and Chemistry n(M∩P∩C) = 12

All the students studying neither Math nor Physics are studying Biology

To find - 1) Students studying biology

              2) Not studying chemistry are studying math but no physics

              3) Studying neither math nor physics nor chemistry

Students studying biology

The formula to find Students studying biology is

n(B) = n(T) - n(M∪P∪C)

The formula to find n(M∪P∪C) is

n(M∪P∪C) = n(M) + n(P) + n(C) - n(M∩P) - n(M∩C) - n(P∩C) +n(M∩P∩C)

n(M∪P∪C) = 60 +51 +54 - 30 - 26 - 21 + 2

n(M∪P∪C) = 100  

Substitute the value of n(M∪P∪C) in the respective formula

n(B) = n(T) - n(M∪P∪C)

n(B) = 130 - 100

n(B) = 30

There are 30 students studying biology

2) Students not studying chemistry are studying math but no physics

Students studying math alone =   60 - (30-12) - (26-12)

Students studying math alone = 60 - 18 - 14

Students studying math alone = 28

There are 28 Students studying math alone

3) Students studying neither math nor physics nor chemistry

Students studying neither math nor physics nor chemistry = n(T)- n(M∪P∪C)

                                                         = 130 - 100

                                                          = 30

There are 30 students studying neither math nor physics nor chemistry  

To learn more ...

1.https://brainly.in/question/116442