O'Reilly logo

Algebra: Abstract and Modern by U. M. Swamy, A. V. S. N. Murthy

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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}

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

  1. AB = {1, 9, 25, 49, 81}
  2. ABC2 = {1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 16, 17, …}
  3. image and XA = A
  4. = {21, 23, 25, 27, 29}
  5. X − (AB) ={2, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required