Help with Cartesian product of power sets please

Nov 2012
3
0
United States
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 2012
3
0
United States
Would it be: { (1,{}), ({},1) } ?
Please see my edit.
And yes the pair is \(\displaystyle (1,\emptyset}).\)
 
Last edited by a moderator:

Plato

MHF Helper
Aug 2006
22,507
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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.