2026-09-08

Exercises for Section 1.3

Source: Richard Hammack, The Book of Proof, 3rd ed., “Exercises for Section 1.3” (p. 15).

A. List all the subsets of the following sets.

• 2. \(\{1,2,\emptyset\}\)

• 6. \(\{\mathbb{R},\mathbb{Q},\mathbb{N}\}\)

B. Write out the following sets by listing their elements between braces.

• 9. \(\left\{X : X\subseteq\{3,2,a\}\text{ and }|X|=2\right\}\)

C. Decide if the following statements are true or false. Explain.

• 13. \(\mathbb{R}^3\subseteq\mathbb{R}^3\)