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Back to Sets

Exercise 1

Avg difficulty 3.0

Let SS be a non-empty set. Determine whether the following statements are true or false.

  1. {1,2}⊂{1,2,3,4}\{1,2\}\subset\{1,2,3,4\}

  2. {1,2,3}⊆{1,2,4}\{1,2,3\}\subseteq\{1,2,4\}

  3. ∅⊆∅\varnothing\subseteq\varnothing

  4. S⊂SS\subset S

  5. S∈{S,∅}S\in\{S,\varnothing\}

  6. {S}∉{S,∅}\{S\}\notin\{S,\varnothing\}

  7. S⊆{S,∅}S\subseteq\{S,\varnothing\} where S≠{∅}S\neq\{\varnothing\}

  8. {S}⊆{S,∅}\{S\}\subseteq\{S,\varnothing\}

Kan, A Complete Introduction to Abstract Algebra, Preliminaries, Sets, Exercise 1

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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.