Mathematical Induction Proof
I cannot get my head around this at all.
Suppose that v is of type Set of Integers and we know the following:-
1. v is sorted.
2. No two items in v are the same.
3. v.at(1) is 12.
For an integer n, where 1 <= n <= v.size(), let p(n) be the following proposition: p(n): v.at(n) => 11 + n.
A. Explain why p(1) is true?
B. suppose that p(k - 1) is true (where 1 < k <= v.size()). Explain why p(k) must then be true.
C. Complete a proof that p(n) is true for all integers n with 1 <= n < v.size().