# 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.

## 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

## Solutions

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.