Mathematics
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.
(i) How many can speak both English and Tamil?
(ii) How many can speak English only?
(iii) How many can speak Tamil only?
Answer
Given:
Total persons in the group: n(E ∪ T) = 50
Persons who can speak English: n(E) = 37
Persons who can speak Tamil: n(T) = 30
(i) How many can speak both English and Tamil?
This represents the intersection of the two sets, n(E ∩ T).
We use the formula:
n(E ∩ T) = n(E) + n(T) - n(E ∪ T)
Substituting the values in above, we get:
n(E ∩ T) = 37 + 30 - 50
n(E ∩ T) = 67 - 50
n(E ∩ T) = 17
∴ 17 persons can speak both English and Tamil.
(ii) How many can speak English only?
This represents the set E - T, consisting of people who speak English but not Tamil.
We use the formula:
n(E - T) = n(E) - n(E ∩ T)
Substituting the values in above, we get:
n(E - T) = 37 - 17
n(E - T) = 20
∴ 20 persons can speak English only.
(iii) How many can speak Tamil only?
This represents the set T - E, consisting of people who speak Tamil but not English.
We use the formula:
n(T - E) = n(T) - n(E ∩ T)
Substituting the values in above, we get:
n(T - E) = 30 - 17
n(T - E) = 13
∴ 13 persons can speak Tamil only.
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