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.