Task 5 Math Systems.docx Task 5 Finite Mathematics Task 5: Math Systems A. Explain why

Task 5 Math Systems.docx  Task 5  Finite Mathematics Task 5: Math Systems  A.  Explain why the set G is closed under the operation #.  The set G = {a, b, c, d}, and is closed under the operation # because the entries in the body of the table are all elements of that set.  B.  Explain why a is the identity element for #.  The identity element is a because each element of the set does not change when you perform the operation # with a. This would be proven by stating that  a ¿ a=a , a ¿ a =a , a ¿ b=b , b ¿ a=b , a ¿ c =c , c ¿ a=c , a ¿ d =d , ∧d ¿ a=d .   This shows the  identity property of the operation #. The column under the a is the same as the column to the left of it, and the row next to the a is the same as the row above it.  C.  Verify two cases of the commutative property.  Commutative property means to change the order in which the operation is performed.  By changing the order, the outcome is still the same.  Here are two examples of this property:  b ¿ c= c ¿ b                                c ¿ d=d ¿ c  b ¿ c= d                                     c ¿ d=b c ¿ b= d                                     d ¿ c=b