Answer to Question 5

dog answer

a. O binary5 G = S
b.  Yes, it is commutative. D binary5 G = G binary5 D. This extends to all possibilities since the table is symmetric with respect to the diagonal line.
c.  The identity element is S. D binary5 S = D. This extends to all elements in the set since all of the values in S's row and column are the same as the row and column headings.
d.  Inverses: What element, when paired with a specific value, will return the identity element S?  The inverse of D is D; the inverse of O is G; the inverse of G is O; and the inverse of S is S.
e.  True
      (D binary5 G) binary5S = D binary5 (G binary5 S)
              O binary5 S = D binary5 G
                      O = O

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