Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incor

1.	Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why? (i) {3, 4} ⊂ A (ii) {3, 4} ∈ A (iii) {{3, 4}} ⊂ A (iv) 1 ∈ A (v) 1⊂ A (vi) {1, 2, 5} ⊂ A (vii) {1, 2, 5} ∈ A (viii) {1, 2, 3} ⊂ A (ix) φ ∈ A (xi) {φ} ⊂ A (x) φ ⊂A
Answer» (i) Incorrect, ∵ 3 ∈ {3, 4} but 3 ∉ A. (ii) Correct, ∵ {3, 4} is a member of A. (iii) Correct, ∵ {3, 4} ∈ A. (iv) Correct, ∵ 1 is a member of A. (v) Incorrect, ∵ 1 is A but not 1⊂ A. (vi) Correct, ∵ 1, 2, 5, ∈ A. (vii) Incorrect, ∵ {1, 2, 5} ∉ A. (viii) Incorrect, ∵ 3 ∈ {1, 2, 3} but 3 ∉ A (ix) Incorrect, ∵ φ ∉ A (x) Correct, ∵ φ is a subset of every set. (xi) Incorrect, ∵ φ ∈ {φ} and φ ∈ A.

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why? (i) {3, 4} ⊂ A (ii) {3, 4} ∈ A (iii) {{3, 4}} ⊂ A (iv) 1 ∈ A (v) 1⊂ A (vi) {1, 2, 5} ⊂ A (vii) {1, 2, 5} ∈ A (viii) {1, 2, 3} ⊂ A (ix) φ ∈ A (xi) {φ} ⊂ A (x) φ ⊂A

Answer»

(i) Incorrect, ∵ 3 ∈ {3, 4} but 3 ∉ A.

(ii) Correct, ∵ {3, 4} is a member of A.

(iii) Correct, ∵ {3, 4} ∈ A.

(iv) Correct, ∵ 1 is a member of A.

(v) Incorrect, ∵ 1 is A but not 1⊂ A.

(vi) Correct, ∵ 1, 2, 5, ∈ A.

(vii) Incorrect, ∵ {1, 2, 5} ∉ A.

(viii) Incorrect, ∵ 3 ∈ {1, 2, 3} but 3 ∉ A

(ix) Incorrect, ∵ φ ∉ A

(x) Correct, ∵ φ is a subset of every set.

(xi) Incorrect, ∵ φ ∈ {φ} and φ ∈ A.