1. ## P(A) interesect P(B)

I wnat to prove that for an sets A and B, P(A) interesect P(B) is not equal to the null set. I know A is an element of P(A) and B is an elemnt of P(B), but where do I go from here?

2. Originally Posted by kathrynmath
I wnat to prove that for an sets A and B, P(A) interesect P(B) is not equal to the null set. I know A is an element of P(A) and B is an elemnt of P(B), but where do I go from here?
$\displaystyle \emptyset$ is a subset of any set

3. Originally Posted by Jhevon
$\displaystyle \emptyset$ is a subset of any set

Yeah, I know that, but what would be a hint on doing the proof?

4. Originally Posted by kathrynmath
Yeah, I know that, but what would be a hint on doing the proof?
That is the proof.

5. Originally Posted by Plato
That is the proof.
Ok, so I say that the null set is a subset of P(A) and P(B). Wouldn't this imply that P(A) interesect P(B)= null set.
I don't know...

6. Originally Posted by kathrynmath
Ok, so I say that the null set is a subset of P(A) and P(B). Wouldn't this imply that P(A) interesect P(B)= null set.
I don't know...
No indeed.
$\displaystyle \left\{ \emptyset \right\} \ne \emptyset$