| I. 150 students were taking at least one juice. |
| II. 225 students were taking neither apple juice nor orange juice. |
A) Only I is true
B) Only II is true
C) Both I and II are true
D) None of these
Correct Answer: B
Solution :
| [b]Let U denote the set of surveyed students and X denote. The set of students taking apple juice and Y denote the set of students taking orange juice, then. |
| \[n(U)=400,\,\,n(X)=100,\,\,n(Y)=150\] And \[n(X\cap Y)=75\] |
| \[n(X\cup Y)=n(X)+n(Y)-n(X\cap Y)\] |
| \[=100+150-75=175\] |
| \[\therefore \] 175 students were taking at least one juice. |
| \[n(X'\cap Y')=n(X\cup Y)'=n(U)-n(X\cup Y)\] |
| \[=400-175=225\] |
| Hence, 225 students were taking neither apple juice nor orange juice. |
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