Concept explainers
Shown in the figure is a 7-hour clock and the table for clock addition in the 7-hour clock system.
|
0 | 1 | 2 | 3 | 4 | 5 | 6 |
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 1 | 2 | 3 | 4 | 5 | 6 | 0 |
2 | 2 | 3 | 4 | 5 | 6 | 0 | 1 |
3 | 3 | 4 | 5 | 6 | 0 | 1 | 2 |
4 | 4 | 5 | 6 | 0 | 1 | 2 | 3 |
5 | 5 | 6 | 0 | 1 | 2 | 3 | 4 |
6 | 6 | 0 | 1 | 2 | 3 | 4 | 5 |
a. How can you tell that the set
is closed under the operation of clock addition?
b. Verify the associative property:
c. What is the identity element in the 7-hour clock system?
d. Find the inverse of each element in the 7-hour clock system.
e. Verify two cases of the commutative property:
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
THINKING MATHEMATICALLY
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage