1. Let L be the set of strings in fa, b}* that contain an even number of a's and also an even number of b's. Let r = (ablba)(aa|bb) (ab|ba)|(aa|bb))". Show that w e L = w e L(r) by strong induction on Jw. Hint: In the inductive step consider a process of removing pairs of symbols from the front of w.

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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.