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.


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