Question

in the college 500 student study maths and 400 study economy if 200 student study both these subjects the find the total no. of student enrolled in college and draw the vein diagram​

Answer 1

Answer:

Let M, P and C denote the students studying Mathematics, Physics and Chemistry

And U represents total students

So, n(U)=200,

n(M)=120,n(P)=90

n(C)=70,n(M∩P)=40,n(P∩C)=30

n(M∩C)=50,n(M∪P∪C)

′

=20

∴n(M∪P∪C)

′

=n(U)−n(M∪P∪C)

⇒20=200−n(M∪P∪C)

⇒n(M∪P∪C)=180

⇒n(M∪P∪C)=n(M)+n(P)+n(C)

−n(M∩P)−n(P∩C)−n(C∩M)+n(C∩M∩P)

∴180=120+90+70−40−30−50+n(C∩M∩P)

⇒180=280−120+n(C∩M∩P)

⇒n(P∩C∩M)=300−280=20

Hence, the number of students studying all three subjects is 20.

Answer 2

Answer:

700

Step-by-step explanation:

Given :- 500 student study maths, 400 study economy and 200 student study both these subjects.

To Find :- The total number of students enrolled in college.

Solution :-

As we know, n( A ∪ B ) = n( A ) + n( B ) - n( A ∩ B )

Let's consider X as total number of students in college.

Consider M and E as sets of maths and economy students.

∴ n( M ) = 500 and n( E ) = 400

Acc. to the question, 200 students study both maths and economy.

∴ n( M ∩ E ) = 200

The above mentioned 200 students have been counted twice in the enrolled list.

Now, the total students who enrolled will be

n( M ∪ E ) = n( M ) + n( E ) - n( M ∩ E )

                = 500 + 400 - 200

                = 900 - 200

                = 700

Therefore, the total number of students enrolled in college are 700.

#SPJ2

https://brainly.in/question/116442

https://brainly.in/question/13798125