MTH 107 Introduction to Finite Mathematics
Worksheet 8/Fall 2015
Name:
8.1 Suppose that cardinal numbers of two sets are n(A) = 101 and n(B) = 92 while the universe
size is n(U ) = 200. If n(A ∪ B) = 177, find n(A ∩ B), n(A ∩ B)′ and draw a Venn diagram
illustrating the composition of U .
A
B
8.2 In a recent health survey, 750 single men were asked to check the appropriate box or boxes on the
following form
2 I am a member of a private gym
2 I am a vegetarian
The results were tabulated as follows: 374 checked the gym box, 92 checked the vegetarian box,
and 332 were blank (no boxes were checked). By drawing a Venn diagram, what percent of these
men were both members of a private gym and vegetarians?
8.3 Determine how many cards, in an ordinary deck of fifty-two, fit the following description: Face
cards or diamonds.
Hint: Face cards are the jack, queen, and king, the ranks of jack to ace are picture cards, and
others are pip value cards. The card with one pip is called an ace.
SOLUTIONS for Quiz 8; MTH107, URI, /Fall 2015
8.1
|A ∩ B| = n(A ∩ B) = |A| + |B| − |A ∪ B| = 101 + 92 − 177 = 16,
|(A ∩ B)′ | = n (A ∩ B)′ = 200 − 16 = 284
200
|A| = 101
|B| = 92
16
76
85
23
750
|V | = 92
|G| = 374
8.2
48
326
44
332
Since |G ∪ V| = 750 − 332 = 418 and |G ∩ V| = |G| + |V| − |G ∪ V| = 48, we have
48
× 100% = 6.4 %
750
8.3 3 × 4 + (13 − 3) = 22