Help with Cartesian product of power sets please

I hope I'm not breaking any rules by posting this, but just came across a homework problem that I was unsure on.

What is the Cartesian product of A and the power set of B if A={1} and B={}?

I know that the Cartesian product of A x B under these cases is the empty set, but it's not the same thing.

So far I've tried looking at it a few different ways: {1} x {{}}= ? being one

Thank you

PS: I'm new here so please be gentle (Angel)

Re: Help with Cartesian product of power sets please

Quote:

Originally Posted by

**chuciulla93** So far I've tried looking at it a few different ways: {1} x {{}}= ? being one

$\displaystyle \{1\}\times\{\emptyset\}$ has one element. What is the ordered pair?

Re: Help with Cartesian product of power sets please

Would it be: { (1,{}), ({},1) } ?

Please see my edit.

And yes the pair is $\displaystyle (1,\emptyset}).$

Re: Help with Cartesian product of power sets please

Re: Help with Cartesian product of power sets please

Quote:

Originally Posted by

**chuciulla93** Please see my edit.

And yes the pair is $\displaystyle (1,\emptyset}).$

I want to explain my edit. Frankly my first reaction was to the title "Cartesian product of power sets please"

But upon rereading the post, that was not being asked.

But was it actually what was meant?

The power set $\displaystyle \mathcal{P}(\emptyset)=\{\emptyset\}$

The power set $\displaystyle \mathcal{P}(\{1\})=\{\emptyset,~\{1\}\}$

Therefore $\displaystyle \mathcal{P}(\{1\})\times \mathcal{P}(\emptyset)=\{(\emptyset,\emptyset),~ ( \{ 1\},\emptyset)\}$: that is two elements.