Let A = {{1,2,3}, {4,5}, {6,7,8}}. Determine which of the following is

1.	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.
Answer» (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.

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.

Answer»

(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.