Question

Let Σ= {a, b}. Give recursive definitions for the following languages over Σ.

Give a recursive definition of the set ODD= {1 3 5 7...}.

Answer 1

The set ODD can be defined recursively as starting with the element 1 and adding 2 to each element.

Step-by-step explanation:

Recursive definition of the set ODD:

The set ODD can be defined recursively as follows:

1. The base case is the element 1, which belongs to ODD.
2. If an element x belongs to ODD, then x+2 also belongs to ODD.

Example: Starting with the base case 1, we can generate the following elements that belong to ODD: 1, 1+2=3, (1+2)+2=5, and so on.