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# 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

**Solution:**

Here are the meanings of ⊂ and ⊄.

If we write A ⊂ B, then we read it as "A is a subset of B" and it means that all the elements of A are present in B.

If we write A ⊄ B, then we read it as "A is NOT a subset of B" and it means that there are some elements of A that are NOT present in B.

It is given that A = {1, 2, {3, 4,}, 5}.

(i) Incorrect as 3 ∈ {3, 4} but 3 ∉ A

(ii) Correct because {3, 4} is an element of A.

(iii) Correct because {3, 4} ∈ {{3, 4}}and {3, 4} ∈ A.

(iv) Correct because 1 is an element of A.

(v) Incorrect because an element of a set can never be a set and hence it cannot be a subset.

(vi) Correct because each element of {1, 2, 5} is also an element of A.

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

(viii) Incorrect because 3 ∈ {1, 2, 3} ; however, 3 ∉ A.

(ix) Incorrect because f is not an element of A.

(x) Correct because f is a subset of every set.

(xi) Incorrect because of Φ = { } and {Φ} = { { } } which is NOT present in A.

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.3 Question 3

## 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

**Summary:**

For A = { 1, 2, { 3, 4 }, 5 }, we are asked to determine which of the given statements are incorrect and why. We found that

(i) {3, 4} ⊂ A is incorrect.

(ii) {3, 4} ∈ A is correct.

(iii) {{3, 4}} ⊂ A

(iv) 1 ∈ A is correct.

(v) 1 ⊂ A is incorrect.

(vi) {1, 2, 5} ⊂ A is correct.

(vii) {1, 2, 5} ∈ A is incorrect.

(viii) {1, 2, 3} ⊂ A is incorrect.

(ix) φ ∈ A is incorrect.

(x) φ ⊂ A is correct.

(xi) {φ} ⊂ A is incorrect.

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