Hi Dr. Peterson,
The exact question is ‘Draw a single Venn diagram that satisfies the the stated condition(s):’
C’ union D = D and (C’ union D’)’ = the empty set
I’m sure I’m wrong about D = the universal set.
So draw a Venn diagram for each of the two conditions (with both B and C being ordinary circles), and determine what relationship each requires. I told you
incorrectly what the first implies, so start fresh for yourself, rather than trust what I've said. Once you've determined how the sets must be related (for example, if you found that [MATH]C\subset D[/MATH]), draw the sets with that relationship (in my [wrong] example, draw C inside D) and make the appropriate shading for each of the two statements. (My understanding is that they don't want shading in the final product, but by doing two separate diagrams with shading, you can show that the conditions are met.
To be honest, I've tried doing this too much in my head, and struggled. In order to be sure I'm not making mistakes, I ended up proving some basic facts, such what it means if [MATH]A\cup B = B[/MATH] or [MATH]A\cup B = U[/MATH] or [MATH]A\cap B = \varnothing[/MATH]. Then I used those to rewrite the given conditions in more basic forms. The answer is sort of like your wrong answer that D = U, in that the sets are not the way you normally draw them.
(As an aside, I learned just a few years ago that, technically, only the generic diagram with circles overlapping in all possible ways is called a Venn diagram; what they are really asking you to draw (as I read it) is an
Euler diagram, in which the actual relationship of the sets is visible. People often use the former term to mean the latter.)