Try It Now

Site: Saylor Academy
Course: CS202: Discrete Structures
Book: Try It Now
Printed by: Guest user
Date: Monday, May 20, 2024, 11:48 PM

Description

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

Table of contents

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. Ac
    8. Cc
    9. A ∩ C
    10. A ⊕ B

  2. 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 = Ac ∩ Bc
    4. A ∪ Ac = U
    5. A ⊆ A ∪ B
    6. A ∩ B ⊆ A

  3. 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}

  4. 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
Creative Commons License 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. {1, 4, 5, 6, 7, 8, 9}
    7. {0, 2, 3, 4, 6, 7, 8}
    8.  ∅
    9. {0}

  2. Answer: These are all true for any sets A, B, and C.

  3. Answer:
    1. {1,4} ⊆ A ⊆ {1, 2, 3, 4}
    2. {2} ⊆ A ⊆ {1, 2, 4, 5}
    3. A = {2, 4, 5}

  4. Answer: