Let A = {ϕ, {ϕ}, 1, {1, ϕ}, 2}. Which of the following are true?
(i) ϕ ∈ A
(ii) {ϕ} ∈ A
(iii) {1} ∈ A
(iv) {2, ϕ} ⊂ A
(v) 2 ⊂ A
(vi) {2, {1}} ⊄A
(vii) {{2}, {1}} ⊄ A
(viii) {ϕ, {ϕ}, {1, ϕ}} ⊂ A
(ix) {{ϕ}} ⊂ A.
(i) True
Φ is a member of set A. Hence, true.
(ii) True
{ Φ} is a member of set A. Hence, true.
(iii) False
1 alone is not a member of A. Hence, false.
(iv) False
We can see that 2 is a member of set A, {2, Φ} is not. Hence, false
(v) True
2 is a member of set A. Hence, true.
(vi) True
{1} is not a member of set A.
(vii) True
Neither {2} and nor {1} is a member of set A. Hence, true.
(viii) True
All three are members of set A. Hence, true.
(ix) False
{{ϕ}} is not a member of set A. Hence, false.