Determine whether each of these statements is true or false. Explain why. 0 ∈ ∅ ∅ ∈ {0} {0} ⊂ ∅ ∅ ⊂ {0} {0} ∈ {0} {0} ⊂ {0} {∅} ⊆ {∅} ∅ ∈ {∅} ∅ ∈ {∅, {∅}} {∅} ∈ {∅} {∅} ∈ {{∅}} {∅} ⊂ {∅, {∅}} {{∅}} ⊂ {∅, {∅}} {{∅}} ⊂ {{∅}, {∅}}

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 28E
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Determine whether each of these statements is true or false. Explain why.

  1. 0 ∈ ∅
  2. ∅ ∈ {0}
  3. {0} ⊂ ∅
  4. ∅ ⊂ {0}
  5. {0} ∈ {0}
  6. {0} ⊂ {0}
  7. {∅} ⊆ {∅}
  8. ∅ ∈ {∅}
  9. ∅ ∈ {∅, {∅}}
  10. {∅} ∈ {∅}
  11. {∅} ∈ {{∅}}
  12. {∅} ⊂ {∅, {∅}}
  13. {{∅}} ⊂ {∅, {∅}}
  14. {{∅}} ⊂ {{∅}, {∅}}
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