Sets Relations And Functions Question 101
Question: In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Then, which of the following is/are true?
I. 150 students were taking at least one juice. II. 225 students were taking neither apple juice nor orange juice.
Options:
A) Only I is true
B) Only II is true
C) Both I and II are true
D) None of these
Show Answer
Answer:
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.
BETA
