Let A-1-2-3-4-5-6-7-8- Determine which of the following is true or false-i 1 - Aii 1-2-3 - Aiii 6-7-8 - Aiv 4-5 - Av - Avi - A

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Standard XI

Mathematics

Jump of a Discontinuity

Let A=1,2,3,4...

Question

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) $ϕ \subset A$

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Solution

(i) False
If it could be 1 $\notin$ A , then it would be true .

(ii) False
The correct form would be $\{1, 2, 3\} \in A or {\{1, 2, 3\}} \subset A$ .

(iii) True

(iv) True

(v) False
A null set is a subset of every set. Therefore, the correct form would be $ϕ \subset A$ .

(vi) True

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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

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.

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 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 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.

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Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: (i) 1∈A (ii) 1, 2, 3⊂A (iii) 6, 7, 8∈A (iv) 4, 5⊂A (v) ϕ∈A (vi) ϕ⊂A

(i) False If it could be 1∉A , then it would be true . (ii) False The correct form would be 1, 2, 3∈A or {1, 2, 3}⊂A. (iii) True (iv) True (v) False A null set is a subset of every set. Therefore, the correct form would be ϕ ⊂ A. (vi) True

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) $ϕ \subset A$

(i) False
If it could be 1 $\notin$ A , then it would be true .

(ii) False
The correct form would be $\{1, 2, 3\} \in A or {\{1, 2, 3\}} \subset A$ .

(iii) True

(iv) True

(v) False
A null set is a subset of every set. Therefore, the correct form would be $ϕ \subset A$ .

(vi) True