Homework: Sets and Counting
Complete the following problems using your textbook:
6.1 Exercise Page 320------2, 10, 28 and 32
6.2 Exercise Page 327------18 and 22
6.3 Exercise Page 334------8
6.4 Exercise Page 344------2, 8, 38 and 40
6.1 Exercise Page 320------2, 10, 28 and 32
In Exercises 1 –4, write the set in set-builder notation.
2. The set of football teams in the NFL
Solution:
{x | x is a football team in NFL}
In Exercises 9–1 4, state whether the statements are true or false.
10. a. A
Answer: FALSE
b. A ⊂ A
Answer: TRUE
In Exercises 27 and 28, shade the portion of the accompanying figure that represents each set.
28. a.
Answer:
b.
Answer:
In Exercises 29–32, shade the portion of the accompanying figure that represents each set.
32. a. A ∪ (B ∩ C)ͨ
Answer:
b. (A ∪ B ∪ C)ͨ
Answer:
6.2 Exercise Page 327------18 and 22
18. Of 100 clock radios with digital tuners and/or CD players sold recently in a department store, 70 had digital tuners and 90 had CD players. How many radios had both digital tuners and CD players?
Solution:
n(digital tuners and CD players) = n(digital tuners)+n(CD players) – n(digital tuners or CD players
n(digital tuners and CD players) = 70 + 90 – 100 = 60
Answer: 60
22. COMMUTER TRENDS Of 50 employees of a store located in downtown Boston, 18 people take the subway to work, 12 take the bus, and 7 take both the subway and the bus. How many employees
a. Take the subway or the bus to work?
n(Take the subway or the bus to work) = n(subway)+n(bus) – n(take both the subway and the bus)
= 18+12- 7 = 23
Answer: 23
b. Take only the bus to work?
n(Take only the bus to work) = 12-7 = 5
c. Take either the bus or the subway to work?
n(Take either the bus or the subway to work) = 23-7 = 16
d. Get to work by some other means?
n(Get to work by some other means) = 50-23 = 27
6.3 Exercise Page 334------8
8. UNION BARGAINING ISSUES In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Five different responses were allowed for each issue. Among completed surveys, how many different responses to this survey were possible?
Solution:
Number of different responses = 5*5*5 = 125
Answer: 125
6.4 Exercise Page 344------2, 8, 38 and 40
In Exercises 1 –22, evaluate the given expression.
2. 2 · 7!
Solution:
2*7! = 2*7*6*5*4*3*2*1= 10080
8. P(5, 3)
Solution:
P(5,3) = 5!/2! = 5*4*3 = 60
38. In how many ways can an investor select four mutual funds for his investment portfolio from a recommended list of eight mutual funds?
Solution:
Number of ways = P(7, 4) = 7!/3! = 7*6*5*4 = 840
40. Find the number of distinguishable permutations that can be formed from the letters of the word PHILIPPINES.
Solution:
number of distinguishable permutations = 11!/(3!3!1!1!1!1!) = 1108800
Answer the following:
• a) What is a Set? Give an example
Solution: A set is a collection of distinct objects normally referred as elements or members. Sets are usually denoted by uppercase letters A,B,C………..and elements or members are denoted by lowercase letters a,b,c,………….
Example: The set of all vowels. {a, e, i, o, u}
• b) When are two sets equal? Give an example of two equal sets.
Solution:
Two sets are equal if they have exactly the same elements.
Example:
A = {1, 2, 3}
B = {2, 3, 1}
Thus A and B are equal sets.
• c) What is the empty set? Give an example.
Solution:
An empty set is a set with no elements. It can be symbolized by {} or ø.
Example: {}