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Question 1. Suppose B is the set of bit strings recursively defined by: 001 ∈ S b ∈ S → 11b ∈ S b ∈ S → 10b ∈ S b ∈ S → 0b ∈ S. Let an the number of bit strings in B of length n, for n ≥ 2. Determine a recursive definition for an, i.e. determine a2, a3 and a recurrence relation. Make sure to justify your recurrence relation carefully. In particular, you must make it clear that you are not double-counting bit strings.

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Question

1.  Suppose B is the set of bit strings recursively defined by:              001 ∈

S

b ∈ S → 11b ∈ S

 b ∈ S → 10b ∈ S

 b ∈ S → 0b ∈ S.

Let an the number of bit strings in B of length n, for n ≥ 2. Determine a recursive definition for an, i.e. determine a2, a3 and a recurrence relation. Make sure to justify your recurrence relation carefully. In particular, you must make it clear that you are not double-counting bit strings.

 
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