Chapter 1.1 Practice

Questions

Question 1

  1. Write out explicitly every element of the following sets
    1. \(\{n\in\mathbb{N}\colon 2n\leq 17\}\)
    2. \(\{n\in\mathbb{N}\colon 3n< 21\}\)
    3. \(\{n\in\mathbb{N}\colon n^2-9< 16\}\)

Question 2

  1. Take \(A=\{2,3,5\}\), \(B=\{1,3,11\}\), \(C=\{1,2,3,11,5\}\), and \(D=\{1,2\}.\) Determine whether or not the following statements are true or false.
    1. \(A\subseteq B\)
    2. \(B\subset A\)
    3. \(A\subseteq C\)
    4. \(A\subset C\)
    5. \(B\subseteq C\)
    6. \(B\subset C\)
    7. \(D\subseteq C\)
    8. \(C\subset D\)
    9. \(D\subset C\)

Question 3

  1. Take \(A=\{1,2,3,4\}\), \(B=\{2,3,4,5\}\), and \(C=\{0,1,5,6\}.\) Write out explicitly the elements of the following sets.
    1. \(A\cup B\)
    2. \(A\cap B\)
    3. \(C\cup B\)
    4. \(C\cap B\)
    5. \(A\cup C\)
    6. \(A\cap C\)
    7. \((A\cap C)\cup B\)
    8. \((B\cap C)\cap A\)

Answers

Question 1

    1. \(\{1,2,3,4,5,6,7,8\}\)
    2. \(\{1,2,3,4,5,6\}\)
    3. \(\{1,2,3,4\}\)

Question 2

    1. false
    2. false
    3. true
    4. true
    5. true
    6. true
    7. true
    8. false
    9. true

Question 3

    1. \(\{1,2,3,4,5\}\)
    2. \(\{2,3,4\}\)
    3. \(\{0,1,2,3,4,5,6\}\)
    4. \(\{5\}\)
    5. \(\{0,1,2,3,4,5,6\}\)
    6. \(\{1\}\)
    7. \(\{1,2,3,4,5\}\)
    8. \(\{\}\)

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