Let p(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. the parts of this exercise outline a strong induction proof that p(n) is true for all integers n ≥ 18.
a) show that the statements p(18), p(19), p(20), and p(21) are true, completing the basis step of a proof by strong induction that p(n) is true for all integers n ≥ 18.
b) what is the inductive hypothesis of a proof by strong induction that p(n) is true for all integers n ≥ 18?
c) what do you need to prove in the inductive step of a proof that p(n) is true for all integers n ≥ 18?
d) complete the inductive step for k ≥ 21.
e) explain why these steps show that p(n) is true for all integers n ≥ 18.