Let A - 1-1- - 2- Which of the following are true -i - Aii - Aiii 1- Aiv 2- - Av 2 - A vi 2-1- Avii 2-1- - Aviii -1- - Aix - A

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Byju's Answer

Standard XII

Mathematics

Subset

Let A =ϕϕ, 1,...

Question

Let A = { $ϕ$ { $ϕ$ }, 1, {1, $ϕ$ }, 2}. Which of the following are true ?

(i) $ϕ ϵ A$ (ii) { $ϕ$ } $ϵ$ A

(iii) {1} $ϵ$ A (iv) {2, $ϕ$ } $\subset$ A

(v) 2 $\subset$ A (vi) {2, {1}} $⊈$ A

(vii) {{2}, {1}}, $⊈$ A

(viii) { $ϕ$ , { $ϕ$ } , {1, $ϕ$ }} $\subset$ A

(ix) {{ $ϕ$ }} $\subset$ A.

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Solution

(i) True, $∵$ $ϕ$ indeed belongs to A.

(ii) True, $∵$ { $ϕ$ } is an element of A.

(iii) False, $∵$ {1} is not an element of A.

(iv) True,

$∵$ {2, $ϕ$ } is a subset of A.

(v) False,

$∵$ 2 is not a subset of A, it is an element of A.

(vi) True, $∵$ {2, {1}} is not a subset of A.

(vii) True, $∵$ {2, {1}} is not a subset of A.

(viii) True, $∵$ { $ϕ$ , { $ϕ$ }, {1, $ϕ$ }} is a subset of A.

(ix) True, $∵$ {{ $ϕ$ }} is a subset of A.

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Similar questions

Q. Let

A = \{ϕ, \{ϕ\}, 1, \{1, ϕ\}, 2\}

. Which of the following are true?
(i)

ϕ \in A

(ii)

\{ϕ\} \in A

(iii)

\{1\} \in A

(iv)

\{2, ϕ\} \subset A

(v)

2 \subset A

(vi)

\{2 \{1\}\} ⊄ A

(vii)

\{\{2\}, \{1\}\} ⊄ A

(viii)

\{ϕ, \{ϕ\}, \{1, ϕ\}\} \subset A

(ix)

\{\{ϕ\}\} \subset A

Q. Let

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

. Which of the following statements are incorrect and why?

(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

Q. Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
(i)

1 \in A

(ii)

\{1, 2, 3\} \subset A

(iii)

\{6, 7, 8\} \in A

(iv)

\{\{4, 5\}\} \subset A

(v)

ϕ \in A

(vi)

ϕ \subset A

Q. Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?
(i)

\{c, d\} \subset A

(ii)

\{c, d\} \in A

(iii)

\{\{c, d\}\} \subset A

(iv)

a \in A

(v)

a \subset A

(vi)

\{a, b, e\} \subset A

(vii)

\{a, b, e\} \in A

(viii)

\{a, b, c\} \subset A

(ix)

ϕ \in A

(x)

\{ϕ\} \subset 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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Let A = {ϕ {ϕ}, 1, {1, ϕ}, 2}. Which of the following are true ? (i) ϕ ϵ A (ii) {ϕ} ϵ A (iii) {1} ϵ A (iv) {2, ϕ} ⊂ A (v) 2 ⊂ A (vi) {2, {1}} ⊈ A (vii) {{2}, {1}}, ⊈ A (viii) { ϕ, {ϕ} , {1, ϕ}} ⊂ A (ix) {{ ϕ}} ⊂ A.