10 Maths -- Set

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)

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

No.of people...