# Try It Now

## Exercises

1. 1. List four elements of each of the following sets:
1. $\left \{ k \in \mathbb{P} \; | \; k - 1 \; \mathrm{is\; a \; multiple\; of\; } 7 \right \}$
2. $\left \{ x \; | \; x \; \mathrm{is\; a\; fruit\; and\; its\; skin\; is\; normally\; eaten} \right \}$
3. $\left \{ x \in \mathbb{Q} \; | \; \frac{1}{x} \in \mathbb{Z} \right \}$
4. $\left \{ 2n \; | \; n \in \mathbb{Z} , n < 0 \right \}$
5. $\left \{ s \; | \; s = 1 + 2+ . . . + n \mathrm{\; for \; some\; n \in \mathbb{P}} \right \}$

2. List all elements of the following sets:
1. $\left \{ \frac{1}{n} \; | \; n \in \left \{ 3,4,5,6 \right \} \right \}$
2. $\left \{ \alpha \in \mathrm{\; the \; alphabet \;} | \; \alpha \mathrm{\; precedes \; F} \right \}$
3. $\left \{ x \in \mathbb{Z} \; | \; x=x+1 \right \}$
4. $\left \{ n^2 \; | \; n = -2,-1,0,1,2 \right \}$
5. $\left \{ n \in \mathbb{P} \; | \; n \; \mathrm{is \; a \; factor \; of \;} 24 \right \}$

3. Describe the following sets using set-builder notation.
1. {5, 7, 9, . . ., 77, 79}
2. the rational numbers that are strictly between -1 and 1
3. the even integers
4. {-18, -9, 0, 9, 18, 27, . . .}

4. Use set-builder notation to describe the following sets:
1. {1, 2, 3, 4, 5, 6, 7}
2. {1, 10, 100, 1000, 10000}
3. {1, 1/2, 1/3, 1/4, 1/5}
4. {0}

5. Let A = {0, 2, 3}, B= {2, 3}, and C = {1, 5, 9}. Determine which of the following statements are true. Give reasons for your answers.
1. $3 \in A$
2. $\left \{ 3 \right \} \in A$
3. $\left \{ 3 \right \} \subseteq A$
4. $B \subseteq A$
5. $A \subseteq B$
6. $\emptyset \subseteq C$
7. $\emptyset \in A$
8. $A \subseteq A$

6. One reason that we left the definition of a set vague is Russell's Paradox. Many mathematics and logic books contain an account of this paradox. Find one such reference and read it. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.