de Morgan's laws on generalised union and intersection.

Hi, I need to prove de Morgan's laws for generalised union and intersections, I came up with a proof but I don't know if it's works with what I know.

Here is what I know:

Given A, a set and B such that then .

is a collection of sets.

.

.

proof:

.

.

Thanks in advance!.

Re: de Morgan's laws on generalised union and intersection.

I think the proof is OK.

I wanted to make a remark about the lack of a quantifier over A in the definition of union, but then I saw that it is a LaTeX error. Since you put existential quantifier in the beginning, I would do the same with the universal quantifier. I would also add an extra equality for clarity, and similarly for intersection.

Hint: use \mid instead of | in the set-builder notation. It creates correct spaces around it.

Re: de Morgan's laws on generalised union and intersection.