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MGF 1106

Chapter 2 Review

For #1 – 14, let U ={a, b, c, d , e, f , g , h} A ={a , b, c, d } B ={a, b, d , e} C ={a, e}

Find each set.

Give a word description for each set. 15. {-3, -1, 1, 3, 5, 7, 9} 16. {January, February, March, … December} Express each set in set-builder notation.

1. A ∪ C

17. {-1, -2, -3, -4, …}

2. B ∩ A

18. {24, 32, 40, 48, …, 88}

3. B ' 4. A − ( B ∩C ')

Place ⊂, ⊆, both, or neither in each blank to make a true statement.

Identify each statement as true or false. Write out the word “true” or “false”.

19. ∅ (x|x is a counting number between 20 and 21}

5. b ∈ A

20. {4, 9, 16}

6. C ⊆ A

For 21 – 23, label and shade each set in an appropriate Venn diagram.

7. B ⊂ ( A ∪ C )

21. X ∪ Y '

8. c ∉ C 9. n[ ( A ∪ B ) − C ] = 4

22. X '∩Y '

10. ∅ ⊂ C 11. A ∩ B ' is equivalent to B ∩ A' 12. ( A ∪B )' = A'∩B ' Find each of the following: 13. n( AXB ) 14. the number of proper subsets of A Name Date

Day/Hour

23. ( X ∪Y ) − Z

{4, 5, 6, 7, 8, 9, 10}

MGF 1106

Chapter 2 Review page 2

24. Is the set {2, 4, 6, 8, …} finite or infinite? 25. Is the set {1/2, 1/4, 1/8, …1/256} finite or infinite? Identify each set as well-defined or not well-defined. 26. {x|x is a good athlete} 27. {x|x is a counting number from 3 to 8} 28. Compact Disc Collection Paula Story is a fan of the music of Paul Simon and Art Garfunkel. In her collection of 22 compact discs, she has the following: 5 on which both Simon and Garfunkel sing 8 on which Simon sings 7 on which Garfunkel sings 12 on which neither Simon nor Garfunkel sings a) How many of her CDs feature only Paul Simon? b) How many of her CDs feature only Art Garfunkel? c) How many feature at least one of these two artists?

29. Student Goals Carol Britz, who sells college textbooks, interviewed freshmen on a community college campus to find out the main goals of today’s students. Let W = the set of those who want to be wealthy, F = the set of those who want to raise a family, E = the set of those who want to become experts in their fields. Carol’s findings are summarized here: n(W) = 160 n(E ∩ F) = 90 n(F) = 140 n(W ∩ F ∩ E) = 80 n(E) = 130 n(E’) = 95 ∩ n(W F) = 95 n[(W ∪ F ∪ E)’] = 10 Find the total number of students interviewed.