# 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

1. 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:
1. A × B
2. B × A
3. A × B × C
4. U × ∅
5. A × Ac
6. B2
7. B3
8. B × $\wp(B)$

2. List all two-element sets in $\wp(\left \{ a, b, c, d \right \})$.

3. How many singleton (one-element) sets are there in $\wp (A)$ if |A| = n ?

4. Let A = {+ , −} and B = {00, 01, 10, 11}.
1. List the elements of A × B
2. How many elements do A4 and (A × B)3 have?

5. Let A and B be nonempty sets. When are A × B and B × A equal?

## Solutions

1. {(0, 2), (0, 3), (2, 2), (2, 3), (3, 2), (3, 3)}
2. {(2, 0), (2, 2), (2, 3), (3, 0), (3, 2), (3, 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)}
4. {(0, 1), (0, 4), (2, 1), (2, 4), (3, 1), (3, 4)}
5. {(2, 2), (2, 3), (3, 2), (3, 3)}
6. {(2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 2, 2), (3, 2, 3), (3, 3, 2), (3, 3, 3)}
7. {(2, ∅), (2, {2}), (2, {3}), (2, {2, 3}), (3, ∅), (3, {2}), (3, {3}), (3, {2, 3})}

2. Answer: {a, b}, {a, c}, {a, d}, {b, c}, {b, d} and {c, d}

3. Answer: There are n singleton subsets, one for each element.