Question
If $$A$$ and $$B$$ are subsets of a set $$X,$$ then what is $$\left\{ {A \cap \left( {X - B} \right)} \right\} \cup B$$ equal to :
A.
$$A \cup B$$
B.
$$A \cap B$$
C.
$$A$$
D.
$$B$$
Answer :
$$A \cup B$$
Solution :
Since, $$A$$ and $$B$$ are subsets of set $$X$$ therefore
$$\eqalign{
& A \subseteq X{\text{ and }}B \subseteq X \cr
& {\text{Consider}}\,\left\{ {A \cap \left( {X - B} \right)} \right\} \cup B \cr
& = \left( {A \cap B'} \right) \cup B \cr
& = A \cup B\,\,\,\,\,\,\,\,\,\left( {\because \,\,B' \cap B = B} \right) \cr} $$