Sets Relations And Functions Question 32
Question: Consider the following statements.
I. If $ A_{n} $ is the set of first n prime numbers, then $ \underset{n=2}{\overset{10}{\mathop{U}}},A_{n} $ is equal to {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} II. If A and B are two sets such that $ n(A\cup B)=50, $ $ n(A)=28,n(B)=32, $ then $ n(A\cap B)=10. $ Which of these is correct?
Options:
A) Only I is true
B) Only II is true
C) Both are true
D) Both are false
Show Answer
Answer:
Correct Answer: C
Solution:
- [c]I. $ \underset{n=2}{\overset{10}{\mathop{U}}},A_{n} $ is the set of first 10 prime numbers $ ={2,3,5,7,11,13,17,19,23,29} $ II. $ n(A\cup B)=n(A)+n(B)-n(A\cap B) $ $ 50=28+32-n(A\cap B) $
$ \Rightarrow n(A\cap B)=60-50=10 $
BETA
