Let A = {{1,2,3}, {4,5}, {6,7,8}}. Determine which of the following is true or false:
(i) 1 A
(ii) {1,2,3} ⊂ A
(iii) {6,7,8} A
(iv) {2, ϕ} ⊂ A
(v) 2 ⊂ A
(vi) {2,{1}} A
(vii) {{2}}, {1}} A
(viii) {ϕ,{ϕ}, {1, ϕ}} ⊂ A.
(i) False
1 is not an element of A.
(ii) True
{1,2,3} ϵ A. this is correct.
(iii) True.
{6, 7, 8} ϵ A.
(iv) False
2 is not an element of A, and ϕ is also not an element of A. Hence, false.
(v) False
2 alone is not an element of A. Hence, false.
(vi) True
{1, 2, 3} is the set belonging to A. {2, {1}} does not belong to A.
(vii) True
{{2}}, {1}} does not belongs to A. Hence, true.
(viii) False
Φ does not belong to A.