SOLUTIONS MANUAL
All Chapters Included
, 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. � = {1,3,5, … }
1.7 1. ={ | } 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: {�, �, �, … , �}
Set builder notation: { | is an upper-case letter of the English alphabet}
EXERCISES
1. Let P represent the set. Then, = {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, = { | is a lizard}
9. Let M represent the set. Then, M = {3�|� is a member of ℕ}
11. Let P represent the set. Then, = { | is an edible plant}
13. ∅ , since no squares are circles.
For more free, peer-reviewed, openly licensed resources visit OpenStax.org.
10/29/25
All Chapters Included
, 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. � = {1,3,5, … }
1.7 1. ={ | } 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: {�, �, �, … , �}
Set builder notation: { | is an upper-case letter of the English alphabet}
EXERCISES
1. Let P represent the set. Then, = {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, = { | is a lizard}
9. Let M represent the set. Then, M = {3�|� is a member of ℕ}
11. Let P represent the set. Then, = { | is an edible plant}
13. ∅ , since no squares are circles.
For more free, peer-reviewed, openly licensed resources visit OpenStax.org.
10/29/25
