Unit 14 Exercises
1. Let Ai = { 1, 2, 3, ..., i } for i = 1, 2, 3, ... . Find
Ai
2. Let Ai = { i, i+1, i+2, ... } for i = 1, 2, 3, ... . Find
Ai
3. Give a recursive definition of the set of positive integers that are multiples of 5.
4. Give a recursive definition of
5. When does a string belong to the set A of bit strings (i.e. strings of 0's and 1's) defined recursively by
Basis Clause: A
Inductive Clause: 0x1 A if x A
where is the empty string (An empty string is a string with no symbols in it.)
Extremal Clause: Nothing is in A unless it is obtained from the Basis and Inductive Clauses.