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In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
- a)30
- b)10
- c)18
- d)28
- e)32
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a class of 40 students, 12 enrolled for both English and German. 22...
Objective: Compute number of students who enrolled for only English
Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.
Then, (A ∪ B) is the set of students who have enrolled for at least one of the two languages.
Because the students of the class have enrolled for at least one of the two languages, we will not find anyone outside A ∪ B in this class.
Therefore, n(A ∪ B) = number of students in the class
So, n(A ∪ B) = 40
Because the students of the class have enrolled for at least one of the two languages, we will not find anyone outside A ∪ B in this class.
Therefore, n(A ∪ B) = number of students in the class
So, n(A ∪ B) = 40
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
i.e., 40 = n(A) + 22 - 12
Or n(A) = 30
n(A) is the number of students who have enrolled for English.
This number is the sum of those who have enrolled for only English and those who have enrolled for both the languages.
Or n(A) = 30
n(A) is the number of students who have enrolled for English.
This number is the sum of those who have enrolled for only English and those who have enrolled for both the languages.
What we have to compute the number of students who have enrolled for only English.
n(only English) = n(English) - n(A ∩ B)
= 30 - 12 = 18.
n(only English) = n(English) - n(A ∩ B)
= 30 - 12 = 18.
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In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?a)30b)10c)18d)28e)32Correct answer is option 'C'. Can you explain this answer?
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