Sets Relations And Functions Question 37
Question: A, B, C and D are four sets such that $ A\cap B=C\cap D=\phi . $ Consider the following:
- $ A\cup B $ and $ B\cup D $ are always disjoint.
- $ A\cap C $ and $ B\cap D $ are always disjoint. Which of the above statements is/are correct?
Options:
A) 1 Only
B) 2 only
C) Both 1 and 2
D) neither 1 nor 2s
Show Answer
Answer:
Correct Answer: B
Solution:
- [b]Let $ A={1,2} $
$ B={3,4,0} $
$ C={5,6,0} $
$ D={7,8} $
Such that $ (A\cap B)=(C\cap D)=\phi $
$ \Rightarrow (A\cup C)={1,2,5,6,0} $
$ \Rightarrow (B\cup D)={3,4,7,8,0} $
$ \Rightarrow (A\cup C)\cap (B\cup D)={0} $
So $ (A\cup C) $ and $ (B\cup D) $ are not always disjoint
$ \Rightarrow (A\cap C)=\phi $ and $ (B\cap D)=\phi $
So $ (A\cap C) $ and $ (B\cap D) $ are always disjoint.
BETA
