Kenneth Rosen Edition 6th Exercise 2.2 Question 8 (Page No. 120)

Question

Determine whether these statements are true or false.

1.  ∅ ∈ {∅}
2.  ∅ ∈ {∅, {∅}}
3. {∅} ∈ {∅}
4. {∅} ∈ {{∅}}
5. {∅} ⊂ {∅, {∅}}
6.  {{∅}} ⊂ {∅, {∅}}
7. {{∅}} ⊂ {{∅}, {∅}}

Comments

Only iii ,is false. Rest all are true

Answer 1

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??