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

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Solution

Given $A = {1, 2, {3, 4}, 5}$
(i) The statement ${3, 4} \subset A$ is incorrect because $3 \in {3, 4}$ ; however, $3 \notin A$ .
(ii) The statement ${3, 4} \in A$ is correct because ${3, 4}$ is an element of A.
(iii) The statement ${{3, 4}} \subset A$ is correct because ${3, 4} \in {{3, 4}}$ and ${3, 4} \in A$ .
(iv) The statement $1 \in A$ is correct because 1 is an element of A.
(v) The statement $1 \subset A$ is incorrect because an element of a set can never be a subset of itself.
(vi) The statement ${1, 2, 5} \subset$ A is correct because each element of ${1, 2, 5}$ is also an element of A.
(vii) The statement ${1, 2, 5} \in A$ is incorrect because ${1, 2, 5}$ is not an element of A.
(viii) The statement ${1, 2, 3} \subset A$ is incorrect because $3 \in {1, 2, 3}$ ; however, $3 \notin A$ .
(ix) The statement $ϕ \in A$ is incorrect because $ϕ$ is not an element of A.
(x) The statement $ϕ \subset A$ is correct because $ϕ$ is a subset of every set.
(xi) The statement ${ϕ} \subset A$ is incorrect because $ϕ ϵ {ϕ}$ ; however, $ϕ \notin A$ .

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Similar questions

A = {1, 2, {3, 4}, 5}

(i) {3, 4} \subset A (i i) {3, 4} \in A

(i i i) {{3, 4}} \subset A (i v) 1 \in A

(v) 1 \subset A (v i) {1, 2, 5} \subset A

(v i i) {1, 2, 5} \in A (v i i i) {1, 2, 3} \subset A

(i x) ϕ \in A (x) ϕ \subset A

(x i) {ϕ} \subset A

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?

(i) {3, 4} $\subset$ A (ii) {3, 4} $\in$ A

(iii) {{3, 4}} $\subset$ A (iv) $1 \in A$

(v) $1 \subset A$ (vi) {1, 2, 5} $\subset$ A

(vii) {1, 2, 5} $\in$ A (viii) {1, 2, 3} $\subset$ A

(ix) $Φ \in A$ (x) $Φ \subset A$

(xi) { $Φ$ } $\subset$ 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

(x) Φ ⊂ A

(xi) {Φ} ⊂ A

Let $A = {1, {2}, {3, 4}, 5}$ . Which of the following are incorrect statements?
Rectify each:

$(i) 2 ϵ A$

$(i i) {2} \subset A$

$(i i i) {1, 2} \subset A$

$(i v) {3, 4} \subset A$

$(v) {1, 5} \subset A$

$(v i) {ϕ} \subset A$

$(v i i) 1 \subset A$

$(v i i i) {1, 2, 3, 4} \subset A$

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