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Concept explainers
Shown in the figure is an 8-hour clock and the table for clock addition in the 8-hour clock system.
|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 0 |
2 | 2 | 3 | 4 | 5 | 6 | 7 | 0 | 1 |
3 | 3 | 4 | 5 | 6 | 7 | 0 | 1 | 2 |
4 | 4 | 5 | 6 | 7 | 0 | 1 | 2 | 3 |
5 | 5 | 6 | 7 | 0 | 1 | 2 | 3 | 4 |
6 | 6 | 7 | 0 | 1 | 2 | 3 | 4 | 5 |
7 | 7 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
a. How can you tell that the set {0, 1, 2, 3, 4, 5, 6, 7} is closed under the operation of clock addition?
b. Verify the associative property:
c. What is the identity element in the 8-hour clock system?
d. Find the inverse of each element in the 8-hour clock system.
e. Verify two cases of the commutative property:
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Chapter 5 Solutions
Thinking Mathematically (7th Edition)
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