JZM1 Finite Mathematics Task 5: Math Systems

Assumptions: The following table represents the operation # on the setG {a, b, c, d}

# a b c d a a b c d

b b c d a

c c d a b

d d a b c

Part A: Explain why G is a closed set under the operation #. G is a closed set under the operation of # because the outcome of the operation is contained in the set of G. According to Blitzer, since all of the elements in the body of the table are elements of G, this is not only a closed set but also an example of clock addition (Blitzer, 2017). Part B: Explain why a is the identity element for #. When looking at the table, a is the identity element...