# Math Help - Cartesian product of universal set.

1. ## Cartesian product of universal set.

Hi, I don't know how to prove this.

$UXA^C = (UXA)^C$

What is the result of UxA? I know AxØ=Ø but have no idea about universal set. Thanks for any help.

2. Originally Posted by truevein
Hi, I don't know how to prove this.

$UXA^C = (UXA^C)$

What is the result of UxA? I know AxØ=Ø but have no idea about universal set. Thanks for any help.
I believe you're trying to prove that $U\times\left(U-A\right)=U-\left(U\times A\right)$. Is that right?

3. Really sorry about the displacement of the parenthesis, I corrected my question.

4. We know that $\left( {\forall x} \right)\left[ {x \in U} \right]$, the universe.

So if $(x,y)\in U\times A^c$ then because $x\in U$ we know $y\notin A$ so $(x,y)\in (U\times A)^c$.

If $(u,w)\in (U\times A)^c$ then $u \notin U \vee w \notin A$.
Again we know that $u\in U$ so $w\notin A$.
So $(u,w)\in U\times A^c$.