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Determine whether these statements are true or false.

  1.  ∅ ∈ {∅}
  2.  ∅ ∈ {∅, {∅}}
  3. {∅} ∈ {∅}
  4. {∅} ∈ {{∅}}
  5. {∅} ⊂ {∅, {∅}}
  6.  {{∅}} ⊂ {∅, {∅}}
  7. {{∅}} ⊂ {{∅}, {∅}}
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Only iii ,is false. Rest all are true
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i think in 7  rhs {{∅}, {∅}} both are same according to set definition only distinct are allowed so it will become {{∅}} now question is 

  1. {{∅}} ⊂ {{∅}} is it proper subset so answer is false. please tell am i thinking right??

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