Algebra: Abstract and Modern

Answers/Hints to Selected Even-Numbered Exercises

CHAPTER 1

EXERCISE 1(A)

2

1. {0, 1, 2, 3, 4, 5}
2. {(−1, 0) ∪ (0, 1) ∩ ℚ
3. {∅, {a}, {c}, {a, c}}
4. {012, 013, …, 019, 023, …, 029, …, 089, 123, 124, …, 129, 134, …, 139, …, }
5. {(0, 0)}
6. ∅, the empty set.

4. X = {1, 2, 3}, ℙ(X) = {∅, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, X}

6. X = {1, 2, 3, …, 100}

A = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} and B = {1, 3, 5, …, 99}

C_i = {i, i + 1, i + 2, i + 3, i + 4} for each 1 ≤ i ≤ 96

1. A ∩ B = {1, 9, 25, 49, 81}
2. A ∪ B ∪ C₂ = {1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 16, 17, …}
3. and X ∩ A = A
4. = {21, 23, 25, 27, 29}
5. X − (A ∪ B) ={2, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, ...