# Try It Now

Site: | Saylor Academy |

Course: | CS202: Discrete Structures |

Book: | Try It Now |

Printed by: | Guest user |

Date: | Tuesday, July 16, 2024, 4:49 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 A
^{4}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.