Try It Now

Work these exercises to see how well you understand this material. Hints and solutions to some of these exercises are given on the second page. As the course proceeds, new notations and terminology will be introduced as they are needed. Be sure to not plug-and-chug answers to the exercises. These are to aid your understanding, and it will be difficult to pass the exam if you do not take the exercises seriously. While you should not copy others' work, feel free to discuss these exercises with others who are taking this course.

Solutions

  1. Answer: (These answers are not unique)
    1. 8, 15, 22, 29
    2. apple, pear, peach, plum
    3. 1/2, 1/3, 1/4, 1/5
    4. -8 , -6, -4, -2
    5. 6, 10, 15, 21

  2. Answer:
    1. \left \{ 2k+1 \; k \in \mathbb{Z}, 2 \leqslant k \leqslant 39 \right \}
    2. \left \{ x \in \mathbb{Q} \; | \; -1 < x < 1 \right \}
    3. \left \{ 2n \; | \; n \in \mathbb{Z} \right \}\
    4. \left \{ 9n \; | \; n \in \mathbb{Z}, -2 \leq n \right \}\ 

  3. Answer:
    1. True
    2. False
    3. True
    4. True
    5. False
    6. True
    7. False
    8. True