2026-09-22

Exercises for Section 2.7

Source: Richard Hammack, The Book of Proof, 3rd ed., “Exercises for Section 2.7” (p. 55).

A. Write the following as English sentences. Say whether they are true or false.

• 1. \(\forall x\in\mathbb{R}, x^2>0\)

• 3. \(\exists a\in\mathbb{R}, \forall x\in\mathbb{R}, ax=x\)

• 6. \(\exists n\in\mathbb{N}, \forall X\in\mathcal{P}(\mathbb{N}), |X|<n\)

• 9. \(\forall n\in\mathbb{Z}, \exists m\in\mathbb{Z}, m=n+5\)