What is $X\cap\mathcal P(X)$? Does the powerset of $X$ contain $X$ as a subset, and thus $X\cap \mathcal{P}(X)=X$, or is $X\cap \mathcal{P}(X)=\emptyset$ since $X$ is a member of the 
$\mathcal{P}(X)$, and not a subset? 

Define a set X={a,b,c} having 3 elements(let).
So, power set of X={{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c},{}}, [i.e it has 2^(3)=8 elements.]
So, X AND P(X) means the common part in 'X' & p(X)
So, X intersection/and P(X)={}
