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) **$\phi ∈A$
**(x) **$\phi⊂ A$
(xi) {$\phi$}$⊂ A$

Answer 1

A = {1, 2, {3, 4}, 5}
(i) The statement {3, 4} $⊂ A$ is incorrect because 3$∈$ {3, 4}; however, $3 ∉ A.$

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(ii) The statement {3, 4}$∈ A$ is correct because {3, 4} is an element of A.

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(iii) The statement {{3, 4}} $⊂ A$ is correct because {3, 4} $∈$ {{3, 4}} and {3, 4}$∈ A.$

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(iv) The statement 1 $∈ A$ is correct because 1 is an element of A.

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(v) The statement 1$⊂ A$ is incorrect because an element of a set can never be a subset of itself.

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(vi) The statement {1, 2, 5} $⊂ A$ is correct because each element of {1, 2, 5} is also an element of A.

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(vii) The statement {1, 2, 5} $∈ A$ is incorrect because {1, 2, 5} is not an element of A.

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(viii) The statement {1, 2, 3} $⊂ A$ is incorrect because $3 ∈$ {1, 2, 3}; however, 3 A.

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(ix) The statement $\phi∈ A$ is incorrect because $\phi$ is not an element of A.

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(x) The statement $\phi ⊂ A$ is correct because $\phi$ is a subset of every set.

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(xi) The statement {$\phi$} $⊂ A$ is incorrect because $\phi ∈$ {$\phi$}; however, $\phi∈ A.$