If $$\left( {A - B} \right) \cup \left( {B - A} \right) = A$$ for subsets $$A$$ and $$B$$ of the universal set $$U,$$ then which one of the following is correct ?
A.
$$B$$ is proper non-empty subset of $$A$$
B.
$$A$$ and $$B$$ are non-empty disjoint sets
C.
$$B = \phi $$
D.
None of the above
Answer :
$$B = \phi $$
Solution :
For subsets $$A$$ and $$B$$ of $$U,$$
If $$\left( {A - B} \right) \cup \left( {B - A} \right) = A,$$
$$ \Rightarrow \,B = \phi $$
Releted MCQ Question on Calculus >> Sets and Relations
Releted Question 1
If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.