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NCERT Class XI Mathematics - Sets - Solutions

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Question : 15 of 73
Marks: +1, -0
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
Solution:  
(i) {3, 4} is a member of set A.
∴ {3, 4} ∈A but 3 ∉ A & 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 and {{3, 4}} is a subset of A.
∴ {{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.
(xi) {f} is not a subset of set A.\ {f} ⊂ A is incorrect.(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 a subset of every set,
∴ ϕ ⊂ A is correct.
(xi) {ϕ} is not a subset of set A.
∴ {ϕ} ⊂ A is incorrect.
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