My question is on how to answer if two statements are equal in set theory. Like De'Morgans laws for example. I'm currently reading James Munkres' book "Topology" and am working through the set theory chapters now, and this isn't the first time I've seen the material, but every time I see this type of work they always use vein-diagrams to "prove" if two statements are the same. I personally don't like vein-diagrams, they don't feel rigourus enough I suppose, so my question is there another way to work on these problems? Like a more algebraic way I suppose, not drawing circles and checking overlapping sections, just isn't the type of math I enjoy.