Practice Problems 1

Lecture 1: Numbers and Sets

Problem numbers refer to the textbook (Chiang & Wainwright, 4th edition). These are not graded, but you should attempt them all before the quiz. Each problem has a Solution toggle: try it yourself first, then expand to check.

Exercise 2.3

1. Write the following in set notation:

1. The set of all real numbers greater than 34.
2. The set of all real numbers greater than 8 but less than 65.

Solution

1. $\{x\in \mathbb{R}\mid x>34\}$, or simply $\{x\mid x>34\}$
2. $\{x\mid 8<x<65\}$

2. Given the sets $S_1=\{2,4,6\}$, $S_2=\{7,2,6\}$, $S_3=\{4,2,6\}$, and $S_4=\{2,4\}$, which of the following statements are true?

1. $S_1=S_3$
2. $S_1=\mathbb{R}$
3. $8\in S_2$
4. $3\notin S_2$
5. $4\notin S_3$
6. $S_4\subset \mathbb{R}$
7. $S_1\supset S_4$
8. $\mathrm{\varnothing }\subset S_2$
9. $S_3\supset \{1,2\}$

Note that $\mathbb{R}$ denotes the set of real numbers.

Solution

(a), (d), (f), (g), and (h) are true.