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
THINK.MATH.LOOSELEAF W/18 WEEK MATHLAB
- 7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect C at their final vertices. (b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C. (c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.arrow_forward1. Let X and Y be random variables and suppose that A = F. Prove that Z XI(A)+YI(A) is a random variable.arrow_forward30. (a) What is meant by the term "product measur"? ANDarrow_forward
- 14. Define X-(H) for a given H E R. Provide a simple example.arrow_forwardLet G be a connected graph with n ≥ 2 vertices. Let A be the adjacency matrix of G. Prove that the diameter of G is the least number d such that all the non-diagonal entries of the matrix A are positive.arrow_forwardfind the general soultion (D-DxDy-2Dx)Z = sin(3x+4y) + x²yarrow_forward
- 3. Show that (a) If X is a random variable, then so is |X|;arrow_forward8. [10 marks] Suppose that 15 people are at a dinner and that each person knows at least 9 of the others. Can the diners be seated around a circular table so that each person knows both of their immediate neighbors? Explain why your answer is correct.arrow_forwarddx Y+2 h dy x + Z " dz X+Z find three Soultion indeparedarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning