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

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- Mar 13th 2008, 07:43 AMKOXKOXKOXSet 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 - Mar 13th 2008, 08:14 AMPlato
**You must redo your posting**!

Read it again. It is impossible for A to equal P(A).

What is B? What does /\ mean? - Mar 13th 2008, 08:26 AMKOXKOXKOX
- Mar 13th 2008, 08:31 AMPlato
Please answer the whole question.

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. - Mar 13th 2008, 08:37 AMKOXKOXKOX
- Mar 13th 2008, 08:53 AMPlato
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 $\displaystyle A \cap B \subseteq A\quad \& \quad A \cap B \subseteq B$.

$\displaystyle X \in P\left( {A \cap B} \right)\quad \Rightarrow \quad X \subseteq A \cap B$