For a set $$A,$$ consider the following statements :
$$\eqalign{
& 1.\,\,A \cup P\left( A \right) = P\left( A \right) \cr
& 2.\,\,\left\{ A \right\} \cap P\left( A \right) = A \cr
& 3.\,\,P\left( A \right) - \left\{ A \right\} = P\left( A \right) \cr} $$
where $$P$$ denotes power set.
Which of the statements given above is/are correct ?
A.
1 only
B.
2 only
C.
3 only
D.
1, 2 and 3
Answer :
1 only
Solution :
Since, Power set is the collection of all the subsets of the set $$A$$ therefore $$AUP\left( A \right) = P\left( A \right)$$
$$\therefore $$ statement (1) 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.