Sets Relations And Functions Question 59
Question: Let X and Y be two non-empty sets such that $ X\cap A=Y\cap A=\phi $ and $ X\cup A=Y\cup A $ for some non-empty set A. Then
Options:
A) X is a proper subset of Y
B) Y is a proper subset of X
C) X = Y
D) X and Y are disjoint sets
Show Answer
Answer:
Correct Answer: C
Solution:
- [c]Suppose $ a\in X $ and $ a\in A\Rightarrow a\in X\cup A\Rightarrow a\in Y\cup A $
$ \Rightarrow a\in Y,anda\in A(\therefore X\cup A=Y\cup A) $
$ \Rightarrow a\in Y\cap A\Rightarrow Y\cap A $ is non-empty This contradicts that $ Y\cap A=\phi $ so, $ X=Y $
BETA
