Surakshya Dhakal • 45 Reads
SetProblems related to two setsQ. In a survey of community, it was found that 70% liked curd, 60% liked milk, 20% didn't like both and 550 people liked both curd and milk. Then,Find the total no. of people participated in the surveyFind the total no. of people who like only curdRepresent it in venn-diagram.Solution:Let U,...
Surakshya Dhakal • 44 Reads
SetProblem involving three setsQ. In a city, three daily newspapers A B and C are published. 42% read newspaper A, 51% read nespaper B, 68% read newspaper C, 30% read newspaper A and B, 28% read neapaper B and C, 36% read A and C, 8% read none of them. Find the percent of people who read all the three papers. Represent the...
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 (A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
n(U) = n (A U B U C) + n (A U B U C)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 languages. • Who can speak both of the languages? • Who can speak at least one language? • Who can speak only one language?
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
ii) n(N∪B) = n(N)+ n(B) - n(N∩B)
= 150 + 80 - 60
iii) n०(N)+ n०(B)= 150-x + 80-x
No.of people speaking both language=60
No.of people speaking at least one language= 170
No.of people speaking only one language= 110