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Clock Arithmetic : Number Properties

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I need to find the definition and give at lease one example in regards to subtraction on clock with arithmetic numbers {1,2,3....12}

A. CLOSED
B. COMMUTATIVE
C. IDENTITY
E. INVERSE

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Solution Summary

Properties of clock numbers are discussed. Arithmetic numbers in clocks are determined.

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Clock arithmetic is arithmetic you do on a clock instead of a number line. In another word, every arithmetic on a clock is done by module 12. In a clock, 12 = 0. The whole set is X = {1,2,...,12=0}.
Now I use some examples to explain it.

A. Closed
For any x, y in X, the addition of x and y is defined as (x+y) module 12 and multiplication of x and y ...

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