If $$\mu $$ is the universal set and $$P$$ is a subset of $$\mu ,$$ then what is $$P \cap \left\{ {\left( {P - \mu } \right) \cup \left( {\mu - P} \right)} \right\}$$ equal to ?
A.
$$\phi $$
B.
$$P'$$
C.
$$m$$
D.
$$P$$
Answer :
$$\phi $$
Solution :
$$\eqalign{
& {\text{Since }}\mu \,{\text{is universal set and }}P \subseteq \mu ,\,P - \mu = \phi \,\,{\text{and }}\mu - P = P' \cr
& {\text{So, }}\left( {P - \mu } \right) \cup \left( {\mu - P} \right) = \phi \cup P' = P' \cr
& {\text{Now, }}P \cap \left\{ {\left( {P - \mu } \right) \cup \left( {\mu - P} \right)} \right\} = P \cap P' = \phi \cr} $$
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.