Help with a Subset Expression

[Biggerboot]

Hi, I was hoping somebody could chime in on this problem and confirm my answer.

It asks, "Which of the diagrams below, left or right, shows a shaded area that represents the expression: [A U B]^c ∩ C (The ^c is the complement)



First image has only C shaded and the second has C, A ∩ C, and B ∩ C.

I believe the second is correct using Demorgan's law, I believe if you distrubute the complement (^C), that would make the expression A^c ∩ B^c ∩ C, so A ∩ C and B ∩ C should be included.

I'm just hoping I could get some confirmation behind this.

 

[Plato]

 

[Biggerboot]

Ah thanks. I was going back and forth on this in my head and couldn't find a solid example from the text (although I think I'll go through it again).