Mathematics
In a city, there are 25 Hindi medium schools, 18 English medium schools and 7 schools have both the mediums. Find
(i) how many schools are there in all in the city ;
(ii) how many schools have Hindi medium only ;
(iii) how many schools have English medium only.
Answer
Given:
Total Hindi medium schools: n(H) = 25
Total English medium schools: n(E) = 18
Schools with both mediums: n(H ∩ E) = 7
(i) how many schools are there in all in the city
This represents the union of the two sets, n(H ∪ E).
We know the formula:
n(H ∪ E) = n(H) + n(E) - n(H ∩ E)
Substituting the values in above, we get:
n(H ∪ E) = 25 + 18 - 7
n(H ∪ E) = 43 - 7
n(H ∪ E) = 36
∴ There are 36 schools in all in the city.
(ii) how many schools have Hindi medium only
This represents the set H - E, consisting of schools that are Hindi medium but not English medium.
We use the formula:
n(H - E) = n(H) - n(H ∩ E)
Substituting the values in above, we get:
n(H - E) = 25 - 7
n(H - E) = 18
∴ 18 schools have Hindi medium only.
(iii) how many schools have English medium only.
This represents the set E - H, consisting of schools that are English medium but not Hindi medium.
We use the formula:
n(E - H) = n(E) - n(H ∩ E)
Substituting the values in above, we get:
n(E - H) = 18 - 7
n(E - H) = 11
∴ 11 schools have English medium only.
Related Questions
Let A and B be two sets such that n(A) = 52, n(B) = 60 and n(A ∩ B) = 16. Draw a Venn diagram and find :
(i) n(A ∪ B)
(ii) n(A - B)
(iii) n(B - A)
Let P and Q be two sets such that n(P ∪ Q) = 70, n(P) = 45 and n(Q) = 38. Draw a Venn diagram and find :
(i) n(P ∩ Q)
(ii) n(P - Q)
(iii) n(Q - P)
There is a group of 50 persons who can speak English or Tamil or both. Out of these persons, 37 can speak English and 30 can speak Tamil.
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(ii) How many can speak English only?
(iii) How many can speak Tamil only?
In a class of 40 students, each one plays either Tennis or Badminton or both. If 28 play Tennis and 26 play Badminton, find
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(ii) how many play Tennis only;
(iii) how many play Badminton only.