comp 1002 assignment 4 more induction please read the following import

Question

COMP 1002
Assignment 4
More Induction!
Please read the following important notes:
Your assignment must be completed on your own.
Sharing solutions, looking for and/or copying solutions from unauthorized sources,
and posting the assignment questions online are all forms of academic misconduct.
Committing an act of academic misconduct will result in a grade of 0
and reported to the department head.
• Only one problem set will be graded and it will be selected at random. Students
who attempt to solve the problem but do not get a perfect score are allowed to
submit a Reflection to obtain bonus marks on their Assignment.
If you do not attempt to solve the selected problem set, then you cannot
submit a reflection.
• Please submit a file for each problem set and clearly state the problem set in the
file's name. Acceptable file formats are PDF, JPG, or PNG.
Do not include your name/id in your submission.
• If your solutions are handwritten, please ensure your solution is legible.
Double check both your image quality and handwriting.
If we cannot read your solution, then you will get a mark of 0.
• While writing your solutions, you will be graded on both your approach and
correctness. A given problem may be solvable in a number of different ways - we
will not grade you on efficiency. That being said, if a problem says to use a specific
technique (i.e. Natural Deduction) then you must solve it using this technique./nWith this understanding please complete the following questions:
1. Theory
A Kirby string is defined recursively as follows:
i) (^o^) is a Kirby string.
ii) (ToT) is a Kirby string.
iii) if A is a Kirby string, then <A> is a Kirby string.
That is concatenated with A concatenated with >.
iv) if A, B, C are all Kirby strings, then A...B...C is a Kirby string.
That is A concatenated with ... concatenated with B concatenated with ...
concatenated with C.
v) Nothing else is a Kirby string.
a) Give a Kirby string that requires the use of rule iv, but such that K₁, K₂, K3
are all different Kirby strings.
Explain how to derive your Kirby string using the rules given.
b) Disprove the following statement:
Every Kirby string has the o character in the centre of the Kirby string.
c) Prove by structural induction that every Kirby string has an odd number of
characters.