How to show A minus B prime or A prime intersect B? Interactions with Circles and the background Primes in venn diagrams

Question

When using regions to find answers for venn diagrams, I come across questions that regions do not work. For instance, Circles do not have the same numbers in prime regions and the circles, so then how can I use those formulas for intersects or removing a circle from the background or showing where they intersect?

 

 

Answer 1

draw 2 circles inside a rectangle; they don't have to be intersecting; label one A and one B; the rectangle is the universe

A-B'

B' means everything in the universe but nothing in B which means everything in A and everything in the rectangle

A-B' means everything in A but not in B', or not "in A and in the universe".

everything in A that is not in A means there are no elements because everything in A is not outside of A

A-B'=the null set, or Ø

 

draw two intersecting circles inside a rectangle

A'∩B

A' means everything in the universe that's not in A

A'∩B means everything in the universe except what's in A, that's also in B, which means everything in B only (which does not include the intersection of A and B-so it's the circle labeled B but not the little tiny piece exactly in the middle where the circles intersect)