Name: ______Class Pd: ______Date: ______
Finite Math B
7.2 PRACTICE: Venn Diagrams & the Union Rule
For #1-12, shade the following Venn Diagrams to represent the indicated set.
1. B∩A' 2. A∪B' 3. A'∪B
4. A'∩B' 5. A'∩B∪A 6. (A∩B)∪(A'∩B')
7. ∅' 8. U' 9. (A∩B)∩C
10. (A∩C')∪B 11. A'∩(B∩C) 12. (C∩B')∩A
For #13 & #14, Use the union rule: nA+nB-nA∩B=n(A∪B) to answer the following:
13. nA=5, nB= 12, nA∩B=4 14. nA∩B=5, nA∪B=38, nA=13
What is nA∪B? What is n(B)?
15. John Smith interviewed 140 people in a suburban shopping center to discover some of their cooking habits. He obtained the following results:
58 use microwave ovens
63 use electric ranges
58 use gas ranges
19 use microwave ovens and electric ranges
17 use microwave ovens and gas ranges
4 use both gas and electric ranges
1 uses all three
2 use none of the three
What is wrong with John Smith’s results?
(Hint: Fill in the Venn Diagram. How many people are represented?)
16. Toward the middle of the harvesting season, peaches for canning come in three types: early, late, and extra late, depending on the expected date of ripening. During a certain week, the following data were recorded at a fruit delivery station:
34 trucks went out carrying early peaches
61 carried late peaches
50 carried extra late
25 carried early and late
30 carried late and extra late
8 carried early and extra late
6 carried all three
9 carried only figs (no peaches at all)
a) How many trucks carried ONLY late variety peaches?
b) How many carried ONLY extra late variety peaches?
c) How many total trucks (IN ALL) went out during the week?
17. After a genetics experiment on 50 pea plants, the number of plants having certain characteristics was tallied, with the following results.
22 were tall
25 had green peas
39 had smooth peas
9 were tall and had green peas
20 had green peas and smooth peas
6 had all three characteristics
4 had none of the characteristics
a) How many plants were tall with smooth peas? (Hint: Use the union rule)
b) How many plants were tall with smooth peas but NOT green peas?
c) How many plants were only tall (without smooth or green peas)?
18. A recent survey of 150 math professors revealed the following:
111 invested in stocks
98 invested in bonds
100 invested in certificates of deposit (CD’s)
80 invested in stocks and bonds
83 invested in bonds and certificates of deposit
85 invested in stocks and certificates of deposit
9 did not invest in any of three
How many professors invested in all three?
The following table lists the number of deaths in the United States during 2003 according to race and gender. Use this information and the letters given to find the number of people in each set?
White(W) / Black
(B) / American Indian
(I) / Asian or Pacific Islander
(A)
Female (F) / 1,078,064 / 143,278 / 6041 / 18,941
Male (M) / 1,025,650 / 148,022 / 7106 / 21,186
19. F∩(I∪A) 20. W'∩M