Use the following table from Example to find the cardinal number of each set.
A ∪ P
Surveying Media Users A media company that produces Pilates videos surveyed its customers to determine whether they would prefer to purchase the videos by buying an access code to allow them to download from a Web site, purchase hard copies on a DVD, or access the videos via a podcast. The company has extracted the following table of information from its customer database:
a) Find the number of elements in M ∪ D.
b) Find the number of elements in A′.
Solution:
a) The number of elements in M ∪ D is the number of people who are middle-aged or prefer DVDs.
n(M ∪ D) = n(M) + n(D)- n(M ∩ D) = 86 + 22 - 8 =100 Thus,
b) A′ is the set of people who do not want to buy an access code, so n(A′) = 63 + 22 = 85
Access code(A) | Podcast(P) | DVD(D) | Total | |
Under 41(Y)oung | 20 | 15 | 9 | 44 |
41 to 55(M)iddle-aged | 44 | 34 | 8 | 86 |
Over55(S)enior | 31 | 14 | 5 | 50 |
Total | 95 | 63 | 22 | 180 |
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