Shown in the figure is a 5-hour clock and the table for clock addition in the 5-hour

Chapter 0, Problem 93

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Shown in the figure is a 5-hour clock and the table for clock addition in the 5-hour system. 0 1 2 3 4 0 0 1 2 3 4 1 1 2 3 4 0 2 2 3 4 0 1 3 3 4 0 1 2 4 4 0 1 2 3 a. How can you tell that the set {0, 1, 2, 3, 4} is closed under the operation of clock addition? b. Verify the associative property: 14 22 3 = 4 12 32 c. What is the identity element in the 5-hour clock system? d. Find the inverse of each element in the 5-hour clock system. e. Verify two cases of the commutative property: 3 4 = 4 3 and 3 2 = 2 3