Answer:a) Show that the statements P(18), P(19), P(20), and P(21) are true,
completing the basis step of the proof.
answer: P(18) = 4 + 7 + 7, P(19) = 4 + 4 + 4 + 7,
P(20) = 4 + 4 + 4 + 4 + 4, P(21) = 7 + 7 + 7,
b) The statement that using just 4-cent and 7-cent stamps we
can form j cents postage for all j with 18 ≤ j ≤ k, where we assume
that k ≥ 21
c. ) Assuming the inductive hypothesis, we can form k + 1 cents
postage using just 4-cent and 7-cent stamps.
d) Because k ≥ 21, we know that P(k − 3) is true, that is,
that we can form k − 3 cents of postage. Put one more 4-cent stamp
on the envelope, and we have formed k + 1 cents of postage.
e) We have completed both the basis step and the
inductive step, so by the principle of strong induction, the statement
is true for every integer n greater than or equal to 18.
Step-by-step explanation:
