How Can I Prove That :
1 - A Is a Subset Or Equal To P(A)
2- P(A/\B) = P(A) /\ P(B)
WHRE A AND B ARE SETS
/\ IS INTERSECTION
Thanks FOR THE HELP IN ADVANCE
How Can I Prove That :
1 - A Is a Subset Or Equal To P(A)
2- P(A/\B) = P(A) /\ P(B)
WHRE A AND B ARE SETS
/\ IS INTERSECTION
Thanks FOR THE HELP IN ADVANCE
Well #1 is FALSE.
The power set of A, P(A), is the collection of all subsets of A.
Now it is true $\displaystyle A \in P(A)$ because $\displaystyle A \subseteq A$.
But cannot happen that $\displaystyle A \subseteq P(A)$.
#2 is simply a matter of noting that $\displaystyle A \cap B \subseteq A\quad \& \quad A \cap B \subseteq B$.
$\displaystyle X \in P\left( {A \cap B} \right)\quad \Rightarrow \quad X \subseteq A \cap B$