Out of 100 students 15 passed in English 12 passed in Mathematics, 8 Science, 4 in English and Science in all the three. Find how many passed in English and Mathematics but not in Science
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Solution
Given n(u)=100
n(E)=15,
n(M)=12,
n(S)=8
n(E∩M)=6,n(M∩S)=7,
n(E∩S)....4,andn(E∩M∩S)=4
a=n(E∩M∩S)=4
a+d=n(M∩S)=7
∴d=3
a+b=n(M∩E)=6
∴b=2
a+c=n(S∩E)=4
∴c=0
a+b+d+e=n(M)=12
∴4+2+3+e=12
∴e=3
a+b+c+g=15
∴4+2+0+g=n(E)=15
∴g=9
a+c+d+f=n(S)=8
∴4+0+3+f=8
∴f=1
The number of students passed in English and Mathematics but not in science b=2