Dept of computer science university of toronto st

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Unformatted text preview: proof, you may make use of any of the equivalences listed on page 30 of the CSC 165 lecture notes — see the course website for a link to the CSC 165 notes online. Dept. of Computer Science, University of Toronto, St. George Campus Page 2 of 2 Solution It is important to note that in structural induction, we do induction on the structure of a recursively defined set of objects. In this case, these are ternary trees. In the base case, we argue that the smallest objects that belong to this set (that are not recursively defined) satisfy the property. In the induction step, we assume that if the “ingredients” satisfy the property then, using the rules of the construction for the set, all the newly constructed elements will also satisfy the property. So, with structural induction, we are not doing induction on any natural number (such as is the case with simple and complete induction). Let’s see this proof now. Basis: The most basic coloured ternary tree is a single node. The single node by definition is both a binary tree and monochromatic. So, it does satisfy the property. Induction Step: Any ternary tree T has to be constructed by taking th...
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