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.
