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Sets Ncert Solutions Maths class 11th Maths Class 11th Sets

15. 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) $? \in$ A

(x) $? \subset$ A

(xi) { $?$ } $\subset$ A

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Answered by

Payal Gupta | Contributor-Level 10

4 months ago

15. (i) False as 3 $\notin$ A and 4 $\notin$ 4. So, {3, 4} $\subset$ A.

(ii) True as {3, 4} $\in$ A. i.e, {3, 4} is an element of A.

(iii) True as {3, 4} $\in$ A so, {3, 4} $\subset$ A.

(iv) True as 1 is an element of A.

(v) False as 1 is not a set so it cannot be a subset of A.

(vi) True as 1 $\in$ A, 2 $\in$ A and 5 $\in$ A. so, {1, 2, 5} $\subset$ A.

(vii) False as {1, 2, 5} is not an element of A.

(viii) False of 3 $\notin$ A.

(ix) False as $?$ is not an element of A.

(x) True, $?$ ? A as $?$ is a subset of every set.

(xi) False, as $?$ is not an element of A.

15. (i) False as 3 <math><mrow><mo>∉</mo></mrow></math> A and 4 <math><mrow><mo>∉</mo></mrow></math> 4. So, {3, 4} <math><mrow><menclose notation="updiagonalstrike"><mrow><mo>⊂</mo></mrow></menclose></mrow></math> A.(ii) True as {3, 4} <math><mrow><mo>∈</mo></mrow></math> A. i.e, {3, 4} is an element of A.(iii) True as {3, 4} <math><mrow><mo>∈</mo></mrow></math> A so, {3, 4} <math><mrow><mo>⊂</mo></mrow></math> A.(iv) True as 1 is an element of A.(v) False as 1 is not a set so it cannot be a subset of A.(vi) True as 1 <math><mrow><mo>∈</mo></mrow></math> A, 2 <math><mrow><mo>∈</mo></mrow></math> A and 5 <math><mrow><mo>∈</mo></mrow></math> A. so, {1, 2, 5} <math><mrow><mo>⊂</mo></mrow></math> A.(vii) False as {1, 2, 5} is not an element of A.(viii) False of 3 <math><mrow><mo>∉</mo></mrow></math> A.(ix) False as <math><mrow><mi>?</mi></mrow></math> is not an element of A.(x) True, <math><mrow><mi>?</mi></mrow></math> ? A as <math><mrow><mi>?</mi></mrow></math> is a subset of every set.(xi) False, as <math><mrow><mi>?</mi></mrow></math> is not an element of A.

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15. 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) ?∈ A (x) ?⊂ A (xi) { ? } ⊂ A

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