Question: a) Define the string set S as follows: Basis step: abc S Recursive step: If x S, then axa S and bxb S and cxc

a) Define the string set S as follows:

Basis step: abc S

Recursive step: If x S, then axa S and bxb S and cxc S

Using structural induction, prove that for each string x S, the length of the string is odd.

b) Use master theorem to find the solution to the recurrence relation f(n) = 4f(n/2) + 2^4, when n = 2^k, where k is a positive integer and f(1) = 1.

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