37 Maths -- Set

Q. In a survey of 120 students, it was found that 17 drink neither tea nor coffee, 88 drink tea and 26 drink coffee. By drawing a venn-diagram, find the number of students who drink both tea and coffee. Given, n(U)=120 n(T)=88 ...

Q. In a survey of 120 students, it was found that 17 drink neither tea nor coffee, 88 drink tea and 26 drink coffee. By drawing a venn-diagram, find the number of students who drink both tea and coffee.

Given,

n(U)=120

n(T)=88

n(C)= 26

n(TuC)= 17

let the number of students who drink both tea and coffee n(TnC) = X

Representing above information in a venn diagram.

From the above Venn diagram,

120=88-X+X+26-X+17

or, 120= 131-X

or, X= 131-120

therefore , X = 11

So, the number of students who drink both tea and coffee is 11.

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There are 150 students in a college of whom 66 play soccer, 27 play exactly two of three sports and 3 play all of three sports. How many of 150 play none of 3 sports?

You might want to retry asking the question. It is unclear, and seems incomplete.

However, when you're dealing with 3 sets, the following formulae might come in handy.

n (AUBUC) =n(A) +n(B) +n(C) -n(AB) -n(AC) -n(BC) + n(ABC)

n(U) =n(AUBUC) +n(AUBUC)^c

where, A, B and C are three non-empty sets,
U denotes the Universal Set

and c (in superscript) indicates complement of a set (Complement of a set: is the difference of a set from the Universal set)

Q. Out of 200 people in a village, 150 can speak Newari language, 80 can speak Bhojpuri, while 30 can't speak any languages. By drawing venn diagram, find the number of people speaking different la...

Let N and B denote the set of people whi can speak Newari and Bhojpuri reapectively.

Now, n(U)=200, n(N)=150, n(B)=80 and(A B)' = 30

i) Let(A B) = x

Representing above information in a venn diagram.

From the venn diagram,

150-x + x +80-x + 30=200

Or, 260-x = 200

Or, x= 260-200

Therefore, x=60.

ii) n(NB) = n(N)+ n(B) - n(NB)

= 150 + 80 - 60

= 170

iii) n(N)+ n(B)= 150-x + 80-x

= 150-60+80-60

= 110

Therefore,

No.of people speaking both language=60

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