Question

Let P(n) be the statement that a postage of n cents can be formed using just 4-cent and 7-cent stamps. Use strong induction to prove that P(n) is true for all integers greater than or equal to some threshold x.

Answer 1

True for n = 18, 19, 20, 21

Explanation:

`P(n) =` a postage of
`n` cents; where
`P(n) = 4x + 7y`. (
`x` are the number of 4-cent stamps and
`y` are the number of 7-cent stamps)

For
`n=18, P(18)` is true.

This is a possibility, if
`x= 1 \ and \ y=2`

`P(18) = 4(1) + 7(2) = 4 + 14 = 18`

Similarly for
`P(19)`:

`P(19) = 4(3) + 7(0) = 19`

`P(20) = 4(5) + 7(0) = 20\\P(21) = 4(0) + 7(3) = 21`