Question

If A = {1, 2, {3, 4}, 5}, then which of the following is incorrect?

• A. {3,4}⊂A
• B. {{3,4}}⊂A
• C. {3,4} ∈ A
• D. None of these

Answer 1

The Correct Option is C

Let A = {1, 2, 3, 4, 5}.
(3) {3, 4} ∈ A  
This statement means that the set {3, 4} is an element of set A. The elements of A are 1, 2, 3, 4, and 5. The set {3, 4} is not an element of A. So, {3, 4} ∈ A is incorrect.

(2) {3, 4} ⊆ A  
This statement means that the set {3, 4} is a subset of A. A subset of A is a set containing only elements that are also in A. The set {3, 4} contains the elements 3 and 4, which are both elements of A. Thus, {3, 4} is a subset of A. So, {3, 4} ⊆ A is correct.

(1) {3, 4} ⊂ A  
This statement means that the set {3, 4} is a proper subset of A. A proper subset of A is a subset of A that is not equal to A. Since {3, 4} is a subset of A and {3, 4} ≠ A, {3, 4} is a proper subset of A. So, {3, 4} ⊂ A is correct.

The incorrect statement is (3).

Final Answer: The final answer is 3