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:
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
THINKING MATHEMATICALLY WITH INTEGRATED
- Example: If ƒ (x + 2π) = ƒ (x), find the Fourier expansion f(x) = eax in the interval [−π,π]arrow_forwardThis box plot represents the score out of 90 received by students on a driver's education exam. 75% of the students passed the exam. What is the minimum score needed to pass the exam? Submitting x and Whickers Graph Low 62, C 62 66 70 74 78 82 86 90 Driver's education exam score (out of 90)arrow_forwardExample: If ƒ (x + 2π) = ƒ (x), find the Fourier expansion f(x) = eax in the interval [−π,π]arrow_forward
- Please can you give detailed steps on how the solutions change from complex form to real form. Thanks.arrow_forwardExamples: Solve the following differential equation using Laplace transform (e) ty"-ty+y=0 with y(0) = 0, and y'(0) = 1arrow_forwardExamples: Solve the following differential equation using Laplace transform (a) y" +2y+y=t with y(0) = 0, and y'(0) = 1arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage