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Question

# 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 (x) Φ⊂A (xi) {Φ} ⊂ A.

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Solution

## (i) {3, 4} is a member of set A. ∴ {3, 4} ∈ A Hence {3, 4} ⊂ A is incorrect. (ii) {3, 4} is a member of set A. ∴ {3, 4} ∈ A is correct. (iii) Here {3, 4} is a member of set A. ∴ {{3, 4}} is a set ∴ {{3, 4}} ⊂ A is correct. (iv) 1 is a member of set A. ∴ 1∈A is correct. (v) 1 is not a set, it is a member of set A. ∴ 1⊂A is incorrect. (vi) 1, 2, 5 are members of set A. ∴ {1, 2, 5} is a subset of set A. ∴ {1, 2, 5} ⊂A is correct. (vii) 1, 2, 5 are members of set A. ∴ {1, 2, 5} is a subset of set A. ∴ {1, 2, 5} ∈A is incorrect. (viii) 3 is not a member of set A. ∴ {1, 2, 3} is not a subset of set A. ∴ {1, 2, 3} ⊂A is incorrect. (ix) Φ is not a member of set A. ∴ Φ∈A is incorrect. (x) Since Φ is subset of every set, ∴ Φ⊂A is correct (xi) Φ is not a member of set A. ∴ {Φ} ⊂A is incorrect.

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