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 n ? 18.a) Show statements P (18), P(19), P(20), and P(21) are true, completing the basis step of the proof.________________b) What is the inductive hypothesis of the proof?________________c) What do you need to prove in the inductive step?________________d) Complete the inductive step for k ? 21.________________e) Explain why these steps show that this statement is true whenever n 18.

Discrete Mathematics CS225 Terms and concepts: Week 2 Reading 145-159, 165-167. 183-184. 201-203 and Lectures and Supplemental Info List of Types of Numbers: • Natural numbers ( ℕ ): Counting numbers. {0, 1, 2, 3…} • Integers ( ℤ ): Positive and negative counting numbers. {…-2, -1, 0, 1, 2, …} • Rational numbers ( ℚ ): Numbers that can be expressed as a ratio of an integer to a non-zero integer. ◦ Quotients of integers. ◦ All integers are rational, but not all rational numbers are integers. • Real numbers ( ℝ ) : Numbers that have decimal representations. ◦ Can be positive, negative, or zero. ◦ All rational numbers are real, not all real numbers are rational. • Irrational numbers (I): Real numbers that are not rationa