Hi, I don't know how to prove this.
$\displaystyle UXA^C = (UXA)^C$
What is the result of UxA? I know AxØ=Ø but have no idea about universal set. Thanks for any help.
Hi, I don't know how to prove this.
$\displaystyle UXA^C = (UXA)^C$
What is the result of UxA? I know AxØ=Ø but have no idea about universal set. Thanks for any help.
We know that $\displaystyle \left( {\forall x} \right)\left[ {x \in U} \right]$, the universe.
So if $\displaystyle (x,y)\in U\times A^c $ then because $\displaystyle x\in U$ we know $\displaystyle y\notin A$ so $\displaystyle (x,y)\in (U\times A)^c$.
If $\displaystyle (u,w)\in (U\times A)^c$ then $\displaystyle u \notin U \vee w \notin A$.
Again we know that $\displaystyle u\in U$ so $\displaystyle w\notin A$.
So $\displaystyle (u,w)\in U\times A^c$.