Question

Give a recursive definition for:
aᶦbʲ

Answer 1

The recursive definition of the given set is provided, explaining that any element must start with at least two 'a's followed by at least one 'b', and the number of 'a's must be at least twice the number of 'b's.

Step-by-step explanation:

The recursive definition of the set i ≥ 2j can be given as:

1. Base Case: a2b0 is in the set.
2. Recursive Case: If an element aibj is in the set, then the element ai+2bj+1 is also in the set.

This recursive definition means that any element in the set must start with at least two 'a's followed by at least one 'b', and the number of 'a's must be at least twice the number of 'b's.