The induction variable 𝑛 will be the depth of a tree. For 𝑛 = 1 we have a tree with only one node (its root). It is simple to check any statement about such a tree :) 1.1. Suppose that for 𝑛 = 1 the statement is true and if it is true for all 𝑘 ≤ 𝑛 then it is true for 𝑛 + 1. Then by the principle of mathematical induction we conclude that the statement is true for all 𝑛 ≥ 1. 1.2. The induction base: for a tree of depth 1 we obviously have leaves(𝑇) = 1, intNodes(𝑇) = 0 and therefore leaves(𝑇) = 2 ∗ intNodes(𝑇) + 1 is true. 1.3, 1.4. The inductive step: su ...
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