Question

Of the 122 students who took a mathematics exam, 76 correctly answered the first question, 60 correctly answered the second question, and 38 correctly answered both questions. How many students answered the first question correctly, but not the second? students answered the first question correctly, but not the second

Answer 1

Answer: 38

Explanation:

• If P and Q are two different set the their difference is given by P-Q i.e. the number of elements in P bit not Q .

i.e.
`P-Q=n(P)-n(P\cap Q)`

Let A be the number of students who correctly answered the first question and B be the number of students who correctly answered the second question .

Given :
`n(A)=76`

`n(B)=60`

`n(A\cap B)=38`

Then the number of students who answered the first question correctly, but not the second is given by :-

`A-B=n(A)-n(A\cap B)\\\\=76-38=38`

Hence, the number of students who answered the first question correctly, but not the second is 38.