Let be the set of all functions from to and define additionand multiplication operations on as follows. For andand Prove thatis a ring.

Funtulis MATH 105 Review of Sets and Properties of Real Numbers 1/25/16 Review of Union and Intersection: Union all of the terms in both sets. Ex. {1,2,3} U {2,3,5} = {1,2,3,5} Intersection the terms that two sets have in common. Ex. {1,2,3} ∩ {1,2} = {1,2} New Sets: Complement all elements not in a named set; represented by the symbol for “prime” ( ‘ ); the set Irrationals is a complement of the set Rationals in the master set Real Numbers. Ex. B = {1,2,5}, so B’ = {3,4,6}. Superset set that contains all of the elements. Ex. The set of Real Numbers are a superset. Venn Diagram: Union: A U B (shown below) Funtulis MATH 105 Intersection: A ∩ B (shown below) Complement of A: A’ (shown below) Prop