Let h be the homomorphism defined by h(a) = 01, h(b) = 10, h(c) = 0, and h(d) = 1. If we take any string w in (0+1)*, h-1(w) contains some number of strings, N(w). For example, h-1(1100) = {ddcc, dbc}, i.e., N(1100) = 2. We can calculate the number of strings in h-1(w) by a recursion on the length of w. For example, if w = 00x for some string x, then N(w) = N(0x), since the first 0 in w can only be produced from c, not from a.

Complete the reasoning necessary to compute N(w) for any string w in (0+1)*. Then, choose the correct value of N(01101).

a) 6

b) 4

c) 16

d) 8

Explain me