In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only.
In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only.
The correct option is C 106
Let M, C, P represent sets of students who had taken mathematics, chemistry and physics respectively From the given information, we have
n(M) = 64 , n(C) = 94, n(P) = 58,
n(MnP) = 28, n(MnC) = 26, n(CnP) = 22
n(MnCnP) = 14
No. of students who had taken only Math
= n(M) - [n(MnP) + n(MnC) - n(MnCnP)]
= 64 - [28+26-14]
= 64 - 40
= 24
No. of students who had taken only Chemistry
= n(C) - [n(MnC) + n(CnP) - n(MnCnP)]
= 94 - [26+22-14]
= 94 - 34
= 60
No. of students who had taken only Physics
= n(P) - [n(MnP) + n(CnP) - n(MnCnP)]
= 58 - [28+22-14]
= 58 - 36
= 22
Total no. of students who had taken only one course
= 24 + 60 + 22
= 106
Let M, C, P represent sets of students who had taken mathematics, chemistry and physics respectively
From the given information, we have
n(M) = 64 , n(C) = 94, n(P) = 58,
n(MnP) = 28, n(MnC) = 26, n(CnP) = 22
n(MnCnP) = 14
No. of students who had taken only Math
= n(M) - [n(MnP) + n(MnC) - n(MnCnP)]
= 64 - [28+26-14]
= 64 - 40
= 24
No. of students who had taken only Chemistry
= n(C) - [n(MnC) + n(CnP) - n(MnCnP)]
= 94 - [26+22-14]
= 94 - 34
= 60
No. of students who had taken only Physics
= n(P) - [n(MnP) + n(CnP) - n(MnCnP)]
= 58 - [28+22-14]
= 58 - 36
= 22
Total no. of students who had taken only one course
= 24 + 60 + 22
= 106
