If \(A=\{1,2\}\) and \(B=\{\{1,2\}\}\), which statement is correct?
Answer and explanation
Correct answer: \(A\in B\)
Set B has exactly one element, and that element is the set \(\{1,2\}\) itself. Since A is the set \(\{1,2\}\), A is therefore an element of B, so \(A\in B\). This does not mean A equals B: A has two numerical elements, whereas B has one set-valued element. Also, B is not a subset of A because its element \(\{1,2\}\) is not the number 1 or 2, and 1 is not directly an element of B.
Frequently asked questions
What is the correct answer to this question?
\(A\in B\)
Why is this the correct answer?
Set B has exactly one element, and that element is the set \(\{1,2\}\) itself. Since A is the set \(\{1,2\}\), A is therefore an element of B, so \(A\in B\). This does not mean A equals B: A has two numerical elements, whereas B has one set-valued element. Also, B is not a subset of A because its element \(\{1,2\}\) is not the number 1 or 2, and 1 is not directly an element of B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
