Sets-Relations-And-Functions Question 142
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
Correct Answer: C $ \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=\emptyset $ so, $ X=Y $
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Answer:
Solution:
BETA
