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Problem 2

Avg difficulty 3.0

Let the set S={1,2,3}S=\{1,2,3\}. Which of the following sets is/are relations on SS? If the set is a relation on SS, is it an equivalence relation?

  1. A=∅A=\varnothing

  2. B={(1,1),(2,2),(3,3)}B=\{(1,1),(2,2),(3,3)\}

  3. C={(1,1),(1,2),(2,2),(3,3)}C=\{(1,1),(1,2),(2,2),(3,3)\}

  4. D={(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3)}D=\{(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3)\}

Kan, A Complete Introduction to Abstract Algebra, Preliminaries, Relations and Functions, Problem 2

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Adapted from A Complete Introduction to Abstract Algebra © 2022–2026 Kan Onn Kit. Licensed under CC BY-SA 4.0. Source: A Complete Introduction to Abstract Algebra. Imported at revision a559e8b.