2026-09-24

Exercises for Section 2.9

Source: Richard Hammack, The Book of Proof, 3rd ed., “Exercises for Section 2.9” (p. 59).

A. Translate each of the following sentences into symbolic logic.

• 1. If \(f\) is a polynomial and its degree is greater than 2, then \(f'\) is not constant.

• 4. For every prime number \(p\), there is another prime number \(q\) with \(q>p\).

• 5. For every positive number \(\varepsilon\), there is a positive number \(\delta\) for which \(|x-a|<\delta\) implies \(|f(x)-f(a)|<\varepsilon\).

• 8. I don’t eat anything that has a face.

Exercises for Section 2.10

Source: Richard Hammack, The Book of Proof, 3rd ed., “Exercises for Section 2.10” (pp. 62–63).

A. Negate the following sentences.

• 3. For every prime number \(p\), there is another prime number \(q\) with \(q>p\).

• 4. For every positive number \(\varepsilon\), there is a positive number \(\delta\) such that \(|x-a|<\delta\) implies \(|f(x)-f(a)|<\varepsilon\).

• 7. I don’t eat anything that has a face.

• 10. If \(f\) is a polynomial and its degree is greater than 2, then \(f'\) is not constant.