If $$A$$ and $$B$$ are two sets then $$\left( {A - B} \right) \cup \left( {B - A} \right) \cup \left( {A \cap B} \right)$$ is equal to :
A.
$$A \cup B$$
B.
$${A \cap B}$$
C.
$$A$$
D.
$$B'$$
Answer :
$$A \cup B$$
Solution :
$$\eqalign{
& \left( {A - B} \right) \cup \left( {B - A} \right) \cup \left( {A \cap B} \right) \cr
& A - B = A \cap B' \cr
& B - A = B \cap A' \cr} $$
$$\left( {A - B} \right) \cup \left( {B - A} \right) = $$ the elements that are only in $$A$$ and $$B$$, which are not common in $$A$$ and $$B$$.
$$\left( {A \cap B} \right) = $$ elements common in $$A$$ and $$B$$.
$$\left( {A - B} \right) \cup \left( {B - A} \right) \cup \left( {A \cap B} \right) = $$ elements in $$A$$ and $$B$$ and common in both $$ = A \cup B$$
Hence, option A is correct.
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.