| 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? |
A) Only I is true
B) Only II is true
C) Both are true
D) Both are false
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. \[n(A\cup B)=n(A)+n(B)-n(A\cap B)\] \[50=28+32-n(A\cap B)\] \[\Rightarrow n(A\cap B)=60-50=10\]
You need to login to perform this action.
You will be redirected in
3 sec
