a How would you show that for any whole number a a 0 a if you were starting from our definition of addition and the audience is your university class b How would you show that for any whole number a a 0 a if you were talking to your class of fourth graders a Choose the correct answer below OA O is the cardinal number of the empty set that is n 0 If the set A has a elements in it n A a then n A n n A U because A and are disjoint But A U A since there are no elements in to add to the set A Thus n A U n A a OB Start with two disjoint sets of the same cardinality A and B with n A n B a Then write the equation Since n A n B a n AUB a Since they are disjoint AnB Then a 0 n AU ANB which is equal to n AUB a OC Use manipulatives to show that the union of a collection with a collection with no elements has the same number of elements as the first collection OD O is the cardinal number of the empty set that is n 0 If the set A has a elements in it n A a then n A n n An because A and are disjoint But An A since there are no elements in to add to the set A Thus n AU n A a