In a class of 60 students, 15 are members of debating club (D), 30 are members of Math club (M) and 20 are members of Science club (S). 3 are members of debating and Math club only. 4 are members of Math club and science club only while 1 is a member of debating and Science club only. 5 are members of all the three clubs. How many students Joined Math or Science club but not debating club?
Answers
The students joined Math or Science club but not debating club = 37
Step-by-step explanation:
Set of students in debating club n(D) = 15
Set of students in Math club n(M) = 30
Set of students in science club n(S) = 20
n(D∩M) = 3
n(M∩S) = 4
n(D∩S) = 1
n(D∩M∩S) = 5
And n(D∪M∪S) = 60
We need to find
How many students joined Math or Science club but not debating club
i.e. n(M∪S) - n(D∩M∩S) - n(D∩S) - n(D∩M)
n(M∪S) = n(M) + n(S) - n(M∩S) -
= 30 + 20 - 4
= 46
Thus,
n(M∪S) - n(D∩M∩S) - n(D∩S) - n(D∩M) = 46 - 5 - 1 - 3 = 37
Hope this answer is helpful.
Know More:
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