course Mth 151
3. {. . . , -4, -3, -2, -1} Solution: E. the set of all negative integers
5. {2, 4, 8, 16, 32}
Solution: B. the set of the five least positive integer powers of 2
6. {. . . , -5, -3, -1, 1, 3, 5, . . .}
Solution: D. the set of all odd integers
9. the set of all counting numbers less than or equal to 6
Solution: { 1, 2, 3, 4, 5 , 6}
10. the set of all whole numbers greater than 8 and less than 18
Solution: { 9, 10, 11, 12, 13, 14, 15, 16, 17}
12. the set of all counting numbers between 4 and 14
Solution: { 5, 6, 7, 8, 9, 10, 11, 12, 13} Type equation here.
15. {-15, -13, -11, . . . . , -1}
Solution: {-9, -7, -5, -3}
16. {-4, -3, -2, . . . . , 4}
Solution: {-1, 0, 1, 2, 3}
18. {90, 87,84, . . . . , 69}
Solution: { 81, 78, 75, 72}
20. { x | x is an odd integer between -8 and 7}
Solution: {-7, -5, -3, -1, 1, 3, 5}
21. the set of all counting numbers greater than 20
Solution: { 21, 22, 23, 24,25, . . . .}
24. the set of U.S. presidents who served after Lyndon Johnson and before George W. Bush
Solution: {Nixon, Ford, Carter, Reagan, H.W. Bush, Clinton}
25. {x| s is a positive multiple of 5}
Solution: {5, 10, 15, 20, 25, 30, . . . .}
27. { x|x is the reciprocal of a natural number}
Solution: irrational numbers are the reciprocal of natural numbers
30. the set of all even natural numbers
Solution: x | x is an even counting number
33. {2, 4, 6, . . .32}
Solution: the set is finite because it ends with 32
35. { ½ , 2/3, ¾, . . .}
Solution: infinite
36. {-10, -8, -6, . . .}
Solution:
37. {x | x is a natural number greater than 50}
Solution: infinite
39. { x | x is a rational number}
Solution: infinite
40. { x | x is a rational number between 0 and 1}
Solution: infinite
42. A={-3, -1, 1, 3, 5, 7, 9}
Solution: n(A)=7
45. A={a, b, c, . . . ., z}
Solution: n(A)= 26
48. the set of current U.S. senators
Solution: n(A)=50
50.A= {1/2, -1/2, 1/3, -1/3, . . ., 1/10, -1/10}
Solution: n(A)=18
51.Explain why it is acceptable to write the statement “x is a vowel in the English alphabet” in the set for Exercise 46, despite the fact that x is a consonant
Solution: X is a consonant in the alphabet, but in the equation “x” represents any possible vowel in the alphabet.
54. {x | x is a negative number}
Solution: well defined; well defined because there are negative numbers
55. {x | x is a good athlete}
Solution: not well defined; not well defined because it is impossible to determine the requirements for a good athlete.
57. { x | x is a difficult course}
Solution: not well defined; not well defined because it is impossible to determine the requirements for a difficult course (even though this course is pretty darn close considering I’m an English major who hasn’t touched math in 4 years}
60. 8 ___{3, -2, 5, 7, 8}
Solution: ∈, the statement is true because 8 is an element of the set.
63. 0___{-2, 0, 5, 9}
Solution: ∈, statement is true because 0 is an element of the set
65. {3}___{2,3,4,6}
Solution: {3} is not an element of this set; this statement is true because {3} is not an element of the set because {3} is a set of its own.
66. {6}___{2+1, 3+1, 4+1, 5+1, 6+1}
Solution: {6} is not an element of this set; this statement is true because {6} is not an element of the set because {6} is a set of its own.
69. 3∈ {2,5,6,8}
Solution: false; 3 is not an element of the set because 3 is not in the set.
70. 6 ∈ {-2,5,8,9}
Solution: false; 6 is not an element in the set because 6 is not in the set
72. m ∈ {l, m, n, o, p}
Solution: true; m is an element of the set because m is in the set
75. {k, c, r, a} = {k, c, a, r}
Solution: true ; because all elements are the same in both sets
78.{3, 7, 12, 14} = {3, 7, 12, 14, 0}
Solution: false ; because both sets don’t have the same elements
80. 4∈ { {3}, {4}, {5} }
Solution: false; because 4 is not an element of the set because the elements of the set are in fact sets themselves
81. { x|x is a natural number less than 3} = {1,2}
Solution: true; because 1 and 2 are natural numbers less than 3
84. 8∈ B= {2, 4, 8, 10}
Solution: true ; because 8 is an element of the set
85. 4 is not an element of C={4, 10, 12}
Solution: false; 4 is an element of C
87.Every element of C={4, 10, 12} is also an element of A={2, 4, 6, 8, 10, 12}
Solution: true; every element of C is also an element of A
90. Explain the difference between a well defined set and a not well defined set. Give examples and use terms introduced in this section.
Solution: I didn’t really know what the exact definitions of the these terms were.
93. Two sets that are equivalent but not equal
Solution: You can have 5 apples in one bag and 5 oranges in another. They are equivalent because they have the same amount of fruit in each bag, but not equal because they are different fruit ; Possible.
95.Volume of Stocks The table lists the ten most active stocks on the New York Stock Exchange in 2004.
2004 Rank|Company name (symbol) |2004 share volume (in millions)
|Lucent Technologies, Inc. (LU) | 581.10
| Nortel Networks Corporations (NT)| 4804.5
|Pfizer, Inc.(PFE) |4430.4
| General Electric Company (GE) |4118.5
| Motorola Inc. (MOT) |2862.5
| Time Warner Inc. (TWX) |2712.8
| Citigroup, Inc. (C) |2649.8
|Texas Instruments, Inc. (TXN) |2559.7
|EMC Corporation (EMC) |2506.7
|AT&T Wireless Services, Inc. (AWE) |2350.0
List the set of issues that had a share volume of at least 4118.5 million
List the set of issues that had a share volume of at most 4118.5 million
Solution (a): {GE, PFE, NT, LU}
Solution (b): { AWE, EMC, TXN, C, TWX, MOT, GE}
96.Burning Calories Alexis Cotton is health conscious, but she does like a certain chocolate bar, each of which contains 220 calories. To burn off unwanted calories, Alexis participates in her favorite activities, shown below, in increments of 1 hour and never repeats a given activity on a given day.
Activity | Symbol |Calories Burned per Hour
Volleyball | v | 160
Golf | g | 260
Canoeing | c | 340
Swimming | s | 410
Running | r | 680
On Monday, Alexis has time for no more than two hours of activities. List all possible sets of activities that would burn off at least the number of calories obtained from three chocolate bars.
Assume that Alexis can afford up to three hours of time for activities on Saturday. List all sets of activities that would burn off at least the number of calories in five chocolate bars.
Solution (a): M={(r,v), (c,s)}
Solution (b): S={r,s,c}
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Very good work.
Note that to say that a set is well-defined is to say that there exists a way of deciding whether a given thing is or is not an element of the set.