AI Tutor
Back to Sets

Exercise 2

Avg difficulty 3.0

Let S={1,2,3,4}S=\{1,2,3,4\}, T={2,3,5}T=\{2,3,5\}, U={(2,2),(3,3),(5,5)}U=\{(2,2),(3,3),(5,5)\}. Determine whether the following statements are true or false.

  1. S∪T={1,2,3,4,5}S\cup T=\{1,2,3,4,5\}

  2. S∪U={1,2,3,(5,5)}S\cup U=\{1,2,3,(5,5)\}

  3. S∩T={2,3}S\cap T=\{2,3\}

  4. T∩U=∅T\cap U=\varnothing

  5. S∖T={1,4}S\setminus T=\{1,4\}

  6. S∖{1,4}=TS\setminus\{1,4\}=T

  7. T2=UT^{2}=U

  8. U⊂(S∪T)2U\subset(S\cup T)^{2}

Kan, A Complete Introduction to Abstract Algebra, Preliminaries, Sets, Exercise 2

AI Tutor

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.