Question

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) \( \phi ∈A\)
(x) \( \phi⊂ A\)
(xi)  {\(\phi\)}\( ⊂ A\)

Answer 1

A = {1, 2, {3, 4}, 5}
(i) The statement {3, 4} \(⊂ A\) is incorrect because 3\(∈\) {3, 4}; however, \(3 ∉ A.\)

---

(ii) The statement {3, 4}\(∈ A\) is correct because {3, 4} is an element of A.

---

(iii) The statement {{3, 4}} \(⊂ A\) is correct because {3, 4} \(∈\) {{3, 4}} and {3, 4}\(∈ A.\)

---

(iv) The statement 1 \(∈ A\)  is correct because 1 is an element of A.

---

(v) The statement 1\(⊂ A\) is incorrect because an element of a set can never be a subset of itself.

---

(vi) The statement {1, 2, 5} \(⊂ A\) is correct because each element of {1, 2, 5} is also an element of A.

---

(vii) The statement {1, 2, 5} \(∈ A\)  is incorrect because {1, 2, 5} is not an element of A.

---

(viii) The statement {1, 2, 3} \(⊂ A\)  is incorrect because \(3 ∈\) {1, 2, 3}; however, 3 A.

---

(ix) The statement \(\phi∈ A\)  is incorrect because \(\phi\) is not an element of A.

---

(x) The statement \(\phi ⊂ A\)  is correct because \(\phi\)  is a subset of every set.

---

(xi) The statement {\(\phi\)} \(⊂ A\) is incorrect because \(\phi ∈\) {\(\phi\)}; however, \(\phi∈ A.\)