How Wide Can the Union Be?

Difficulty: Medium · Topics: Discrete Mathematics, Sets, Venn Diagrams

n(A)=7, n(B)=4

Which of the following statements are true?

I. n(Acup B) can be at most 11.

II. n(Acup B) can be as small as 6.

III. If Acap B≠varnothing, then n(Acup B) can be at most 9.

IV. If Bnotsubseteq A, then n(Acup B) is at least 8.