# Help with Cartesian product of power sets please

• Nov 25th 2012, 03:57 AM
chuciulla93
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)
• Nov 25th 2012, 04:07 AM
Plato
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?
• Nov 25th 2012, 04:22 AM
chuciulla93
Re: Help with Cartesian product of power sets please
Would it be: { (1,{}), ({},1) } ?
And yes the pair is $\displaystyle (1,\emptyset}).$
• Nov 25th 2012, 05:04 AM
chuciulla93
Re: Help with Cartesian product of power sets please
Thank you
• Nov 25th 2012, 08:08 AM
Plato
Re: Help with Cartesian product of power sets please
Quote:

Originally Posted by chuciulla93
And yes the pair is $\displaystyle (1,\emptyset}).$
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.