Try It Now

Exercises

1. Let A = {0, 2, 3}, B = {2, 3}, C = {1, 5, 9}, and let the universal set be U = {0, 1, 2, ..., 9} . Determine:
   1. A ∩ B
   2. A ∪ B
   3. B ∪ A
   4. A ∪ C
   5. A − B
   6. B − A
   7. A^c
   8. C^c
   9. A ∩ C
   10. A ⊕ B
       
       
3. Let U = {1, 2, 3, ..., 9}. Give examples of sets A, B, and C for which:
   1. A ∩ (B ∩ C) = (A ∩ B) ∩ C
   2. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
   3. (A ∪ B)^c = A^c ∩ B^c
   4. A ∪ A^c = U
   5. A ⊆ A ∪ B
   6. A ∩ B ⊆ A
      
      
5. What can you say about A if U = {1, 2, 3, 4, 5}, B = {2, 3}, and (separately)
   1. A ∪ B = {1, 2, 3, 4}
   2. A ∩ B = {2}
   3. A ⊕ B = {3, 4, 5}
      
      
7. 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:
   1. evening students
   2. undergraduate mathematics majors
   3. non-math graduate students
   4. non-math undergraduate students
      
      

Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

Solutions

1. Answer:
   1. {2, 3}
   2. {0, 2, 3}
   3. {0, 2, 3}
   4. {0, 1, 2, 3, 5, 9}
   5. {0}
   6. ∅
   7. {1, 4, 5, 6, 7, 8, 9}
   8. {0, 2, 3, 4, 6, 7, 8}
   9.  ∅
   10. {0}
       
       
3. Answer: These are all true for any sets A, B, and C.
   
   
5. Answer:
   
   1. {1,4} ⊆ A ⊆ {1, 2, 3, 4}
   2. {2} ⊆ A ⊆ {1, 2, 4, 5}
   3. A = {2, 4, 5}
      
      
7. Answer:
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