# Set Theory : Help Needed Plz

• March 13th 2008, 07:43 AM
KOXKOXKOX
Set Theory : Help Needed Plz
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
• March 13th 2008, 08:14 AM
Plato
Read it again. It is impossible for A to equal P(A).
What is B? What does /\ mean?
• March 13th 2008, 08:26 AM
KOXKOXKOX
Quote:

Originally Posted by Plato
Read it again. It is impossible for A to equal P(A).
What is B? What does /\ mean?

/\ MEANS INTERSECTION
• March 13th 2008, 08:31 AM
Plato
What is B?
Do you mean A is a subset of B or of P(B)?
As it is, the question is not yet clear.
• March 13th 2008, 08:37 AM
KOXKOXKOX
Quote:

Originally Posted by Plato
What is B?
Do you mean A is a subset of B or of P(B)?
As it is, the question is not yet clear.

I HAVE TO Prove That :

given any set A, then i have to prove that
A Is a Subset Or Equal To P(A)

given any 2 sets A and B , then i have to prove that
2- P(A/\B) = P(A) /\ P(B)

/\ IS INTERSECTION
Thanks FOR THE HELP IN ADVANCE
• March 13th 2008, 08:53 AM
Plato
Well #1 is FALSE.
The power set of A, P(A), is the collection of all subsets of A.
Now it is true $A \in P(A)$ because $A \subseteq A$.
But cannot happen that $A \subseteq P(A)$.

#2 is simply a matter of noting that $A \cap B \subseteq A\quad \& \quad A \cap B \subseteq B$.
$X \in P\left( {A \cap B} \right)\quad \Rightarrow \quad X \subseteq A \cap B$