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 Show solution toggle: try it yourself first, then expand to check.

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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.
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  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. \(\emptyset \subset S_2\)
  9. \(S_3 \supset \{1,2\}\)

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

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