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

The parts of the question are solved below:

(i) Here, we know that {3, 4} is a member of set A.

= {3, 4} ∈ A

Thus, the given statement is incorrect.

(ii) Here, we know that {3, 4} is a member of set A.

Thus, the given statement is incorrect.

(iii) Here, we know that {3, 4} is a member of set A.

={{3, 4}} is a set.

Thus, the given statement is correct.

(iv) Here, we can observe that 1 is a member of set A.

Thus, the given statement is correct.

(v) Here, we can see that 1 is a member of set A but is not any set itself.

Thus, the given statement is incorrect.

(vi) Here, we can see that 1, 2, 5 is a member of set A

Thus, the given statement is correct.

(vii) Here, we can see that 1, 2, 5 is a member of set A

=, {1, 2, 5} is a subset of A

Thus, the given statement is incorrect.

(viii) Here, we can see that 3 is not a member of set A

={1, 2, 3} is not a subset of A

Thus, the given statement is incorrect.

(ix) Here, we can see that ϕ is not a member of set A

Thus, the given statement is correct.

(x) Here, we can see that ϕ is not a member of set A

Thus, the given statement is incorrect.