Contemporary Mathematics (1st Edition, 2024) – Solutions Manual – by Kirk

ALL 13 CHAPTERS COVERED




SOLUTIONS MANUAL

,
,Contemporary Mathematics



Chapter 1
Sets

Solutions
1.1 Basic Set Concepts

YOUR TURN
1.1 1. Answers may vary. One possible solution: T = {wrench, screwdriver, hammer, plyers}
1.3 1. ∅ or { }. No numbers are divisible by 0.
1.5 1. 𝑀 = {1,3,5, … }
1.7 1. 𝐼 = { 𝑖 | 𝑖 𝑖𝑠 𝑎 𝑚𝑢𝑠𝑖𝑐𝑎𝑙 𝑖𝑛𝑠𝑡𝑟𝑢𝑚𝑒𝑛𝑡} Since listing out every musical instrument is a tedious,
and perhaps difficult task, the solution should have this form (set builder).
1.9 1. We can count up the elements of B. Thus, B is finite.
2. We cannot count up the number of elements in the real numbers and ever finish. Thus, ℝ is
infinite.

CHECK YOUR UNDERSTANDING
1. set
3. This is not a well-defined set. Whether a restaurant is in the top five is a matter of opinion, not a
fact.
5. n(A) = 12 and n(B) = 12. However, apples and donuts are different. Thus, A is equivalent to B but
they are not equal. We can write this as: A ~ B, but A ≠ B.
7. Roster method: {𝐴, 𝐵, 𝐶, … , 𝑍}
Set builder notation: {𝑥|𝑥 is an upper-case letter of the English alphabet}

EXERCISES
1. Let P represent the set. Then, 𝑃 = {red, yellow, blue}
3. Let A represent the set. Then, A = {50,51,52, … ,100}.
5. Let C represent the set. Then, C = {king, queen, rook, knight, bishop, pawn}
7. Let L represent the set. Then, 𝐿 = {𝑙|𝑙 is a lizard}
9. Let M represent the set. Then, M = {3𝑛|𝑛 is a member of ℕ}
11. Let P represent the set. Then, 𝑃 = {𝑝|𝑝 is an edible plant}
13. ∅ , since no squares are circles.
15. Let C represent the set. Then, C = {Greg, Peter, Bobby, Marsha, Jan, Cindy}


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, Contemporary Mathematics

17. ∅, since no polar bears live in Antarctica.
19. Let B represent the set. 𝐵 = {𝑏|𝑏 is a children's book written and illustrated by Mo Willems}
(You could write out all the book titles and use the roster method, but this would be a very long
list. Try to choose the shortest method for writing a set that still makes the set well-defined.)
21. Because we can list out all of the character names in the book, this is a well-defined set.
23. The size of the group, the definition of “old”, and the definition of “new tricks” is not given and
are all subject to opinion. This set is not well-defined.
25. Since zebras cannot fly an airplane, this is the empty set. Thus, this is a well-defined set.
27. 𝑛(𝑃) = 6
29. 𝑛(∅) = 0
31. 𝑛(𝐹) = 9
33. 𝑛(𝐶) = 𝑛(ℕ) = ℵ0
35. 𝑛(𝐿) = 14
37. 𝑛(𝐴) = 𝑛({right, acute, obtuse}) = 3; 𝑛(𝐵) = 𝑛({equilateral, scalene, isoceles}) = 3
Since both sets contain 3 elements, the two sets are equivalent. But the elements of the sets are
not the same, so the two sets are not equal.
Thus, A ~ B
39. 𝑛(𝐴) = 𝑛({red, orange, yellow}) = 3; 𝑛(𝐵) = 𝑛({green, blue, indigo, violet}) = 4. Since they
do not contain the same number of elements, they are neither equivalent nor equal.
41. 𝑛(𝐴) = 𝑛({−2, −1,0, … }) = ℵ0 ; 𝑛(𝐵) = 𝑛({2,3,5, … }) = ℵ0 . The two sets do not contain the
same elements since A contains 0 (for example) and B does not. However, they both have the
same number of elements. Thus, A ~ B.
43. 𝐴 = ∅; 𝐵 = { }. Since these are both the empty set, both sets contain 0 elements. Thus A = B.
45. The set of natural numbers is an infinite set.
47. We could count or list out all the jazz venues in New Orleans, Louisiana, and we would finish.
Thus, this set is finite.
49. We could count or list out all of the different types of cheeses and we would finish. Thus, this set
is finite.

1.2 Subsets

YOUR TURN
1.11 1. {heads, tails}; {heads}, {tails}; and ∅
1.13 1. E is a subset of ℕ, so 𝐸 ⊂ ℕ.
1.15 1. Multiples of 5 can be written as 5n. So, {5, 10, 15, … } = {𝑚|𝑚 = 5𝑛 where 𝑛 ∈ ℕ}.




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