If \(A=\{1,\{1,2\},3\}\), which statement is false?
Answer and explanation
Correct answer: \(\{1,2\}\subseteq A\)
The elements of A are 1, the set \(\{1,2\}\), and 3. Thus 1 is an element of A, and \(\{1,2\}\) is also an element of A, so options A and B are true. However, for \(\{1,2\}\subseteq A\), both 1 and 2 would have to be elements of A. Although 1 is in A, 2 is not a separate element of A; it occurs only inside the nested set \(\{1,2\}\). Therefore option C is false. Every set is a subset of itself, so D is true.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2\}\subseteq A\)
Why is this the correct answer?
The elements of A are 1, the set \(\{1,2\}\), and 3. Thus 1 is an element of A, and \(\{1,2\}\) is also an element of A, so options A and B are true. However, for \(\{1,2\}\subseteq A\), both 1 and 2 would have to be elements of A. Although 1 is in A, 2 is not a separate element of A; it occurs only inside the nested set \(\{1,2\}\). Therefore option C is false. Every set is a subset of itself, so D is true.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
