Discrete Structures

– You must justify your answers.
– The answers should be concise, clear and neat.
– When presenting proofs, every step should be justified.

Question 4: In class, we have seen that for any integer m 1, the number of 00-free bitstrings of length m is equal to m+2, wh

Question 4: In class, we have seen that for any integer m 1, the number of 00-free bitstrings of length m is equal to m+2, which is the (m2)-th Fibonacci number Let n 2 2 be an int eger. For each of the fol lowing, justily your answer . How many 00-free bitstrings of length n do not contain any 0? How many 00-free bitstrings of length n have the following property: The rightmost 0 is at position How many 00-free bitstrings of length n have the following property: The rightmost 0 . Let k be an integer with 3 3k. How many 00-free bitstrings of length n have the . Use the previous results to prove that is at position 2. following property: The rightmost 0 is at position k k. k=1 Show transcribed image text