Question

in a survey of university students, 64 had taken mathematics course, 94 had taken computer science course, 58 had taken physic course, 28 had taken mathematic and physic, 26 had taken mathematic and computer science, 22 had taken computer science and physic course and 14 had taken all the three course. find the number of students who were surveyed.to find how many had taken one course only​

Answer 1

➠Solution:-

⇒Step 1 :

Let M, C, P represent sets of students who had taken mathematics, chemistry and physics respectively

⇒Step 2 :

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

⇒Step 3 :

From the basic stuff, we have

No. of students who had taken only Math

=  n(M) - [n(MnP) + n(MnC) - n(MnCnP)]

=  64 - [28 + 26 - 14]

=  64 - 40

=  24

⇒Step 4 :

No. of students who had taken only Chemistry :

                 = n(C) - [n(MnC) + n(CnP) - n(MnCnP)]

                 = 94 - [26+22-14]

                 = 94 - 34

                 = 60

⇒Step 5 :

No. of students who had taken only Physics :

=  n(P) - [n(MnP) + n(CnP) - n(MnCnP)]

=  58 - [28 + 22 - 14]

=  58 - 36

=  22

⇒Step 6 :

Total no. of students who had taken only one course :

                                   =  24 + 60 + 22

                                  =  106

Hence, the total number of students who had taken only one course is 106.