If \(A=\{1,\{1,2\},3\}\), which statement is false?
Answer and explanation
Correct answer: \(\{1,2\}\subseteq A\)
The set A contains three elements: 1, the nested set \(\{1,2\}\), and 3. Therefore 1 and 3 are individual elements of A, making option C true. The nested set \(\{1,2\}\) itself is also an element of A, so option B is true. But option D claims that both 1 and 2 are elements of A. The element 2 is not separately in A; it appears only inside the nested set. Hence D is the false statement.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2\}\subseteq A\)
Why is this the correct answer?
The set A contains three elements: 1, the nested set \(\{1,2\}\), and 3. Therefore 1 and 3 are individual elements of A, making option C true. The nested set \(\{1,2\}\) itself is also an element of A, so option B is true. But option D claims that both 1 and 2 are elements of A. The element 2 is not separately in A; it appears only inside the nested set. Hence D is the false statement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
