Try It Now
Site: | Saylor Academy |
Course: | CS202: Discrete Structures |
Book: | Try It Now |
Printed by: | Guest user |
Date: | Monday, December 4, 2023, 12:54 AM |
Description
Work these exercises to see how well you understand this material.
Exercises
- Let A = {0, 2, 3}, B = {2, 3}, C = {1, 4}, and let the universal set be U = { 0, 1 , 2 , 3 , 4 }. List the elements of:
- List all two-element sets in
.
- How many singleton (one-element) sets are there in
if |A| = n ?
- Let A = {+ , −} and B = {00, 01, 10, 11}.
- List the elements of A × B
- How many elements do A4 and (A × B)3 have?
- Let A and B be nonempty sets. When are A × B and B × A equal?
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
- Answer:
- {(0, 2), (0, 3), (2, 2), (2, 3), (3, 2), (3, 3)}
- {(2, 0), (2, 2), (2, 3), (3, 0), (3, 2), (3, 3)}
- {(0, 2, 1), (0, 2, 4), (0, 3, 1), (0, 3, 4), (2, 2, 1), (2, 2, 4), (2, 3, 1), (2, 3, 4), (3, 2, 1), (3, 2, 4), (3, 3, 1), (3, 3, 4)}
- ∅
- {(0, 1), (0, 4), (2, 1), (2, 4), (3, 1), (3, 4)}
- {(2, 2), (2, 3), (3, 2), (3, 3)}
- {(2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 2, 2), (3, 2, 3), (3, 3, 2), (3, 3, 3)}
- {(2, ∅), (2, {2}), (2, {3}), (2, {2, 3}), (3, ∅), (3, {2}), (3, {3}), (3, {2, 3})}
- Answer: {a, b}, {a, c}, {a, d}, {b, c}, {b, d} and {c, d}
- Answer: There are n singleton subsets, one for each element.
- Answer:
- {+00, +01, +10, +11, −00, −01, −10, −11}
- 16 and 512
- Answer: They are equal when A = B.