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Completion requirements

Work these exercises to see how well you understand this material.

- Let A = {0, 2, 3}, B = {2, 3}, C = {1, 5, 9}, and let the universal set be U = {0, 1, 2, ..., 9} . Determine:
- A ∩ B
- A ∪ B
- B ∪ A
- A ∪ C
- A − B
- B − A
- A
^{c} - C
^{c} - A ∩ C
- A ⊕ B

- Let U = {1, 2, 3, ..., 9}. Give examples of sets A, B, and C for which:
- A ∩ (B ∩ C) = (A ∩ B) ∩ C
- A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
- (A ∪ B)
^{c}= A^{c}∩ B^{c} - A ∪ A
^{c}= U - A ⊆ A ∪ B
- A ∩ B ⊆ A

- What can you say about A if U = {1, 2, 3, 4, 5}, B = {2, 3}, and (separately)
- A ∪ B = {1, 2, 3, 4}
- A ∩ B = {2}
- A ⊕ B = {3, 4, 5}

- Given that U = all students at a university, D = day students, M = mathematics majors, and G = graduate students. Draw Venn diagrams illustrating this situation and shade in the following sets:
- evening students
- undergraduate mathematics majors
- non-math graduate students
- non-math undergraduate students

Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf

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