Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write each set in roster form and in set-builder notation.

9. M is the set of integers that are greater than − 1 negative 1  and less than 4.
10. N is the set of real numbers that are factors of 12.
11. P is the set of natural numbers that are less than 11.
12. R is the set of even natural numbers that are less than 2.

See Problem 2.

Write the solutions of each inequality in set-builder notation.

13. 4 y + 7 ≥ 23 4 y plus 7 greater than or equal to 23
14. 5 r + 8 < 63 5 r plus 8 less than 63
15. 13 − 9 m < 58 13 minus 9 m less than 58
16. 7 − 3 d ≥ 28 7 minus 3 d greater than or equal to 28
17. 2 ( 3 p − 11 ) ≥ − 16 2 open 3 p minus 11 close greater than or equal to negative 16
18. 3 ( 2 k + 12 ) < − 42 3 open 2 k plus 12 close less than negative 42

See Problem 3.

List all the subsets of each set.

19. {a, e, i, o}
20. {0, 1, 2}
21. {dog, cat, fish}
22. { − 2 , negative 2 comma  2}
23. {1}
24. { + , − , × , ÷ } the set plus comma negative comma times comma divides end set

See Problem 4.

25. Suppose U = {1, 2, 3, 4, 5} is the universal set and A = {2, 3}. What is A'?
26. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {2, 4, 6, 8}. What is P '?
27. Suppose U = {…, − 3 , negative 3 comma   − 2 , negative 2 comma   − 1 , negative 1 comma  0, 1, 2, 3, …} is the universal set and R = {…, − 3 , negative 3 comma   − 1 , negative 1 comma  1, 3, …}. What is R'?
28. Suppose U = {1, 2} is the universal set and T = {1}. What is T '?

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