If \(A=\{\emptyset,\{\emptyset\},1\}\), which of the following is not a subset of \(A\)?
Answer and explanation
Correct answer: \(\{1,2\}\)
A set is a subset of \(A\) only when each of its elements is also an element of \(A\). The elements of \(A\) are \(\emptyset\), \(\{\emptyset\}\), and \(1\). Options A, B, and C contain only elements from this list, so they are subsets of \(A\). Option D contains the element \(2\), but \(2\notin A\); therefore \(\{1,2\}\) is not a subset. Notice especially that \(\emptyset\) and \(\{\emptyset\}\) are different objects.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2\}\)
Why is this the correct answer?
A set is a subset of \(A\) only when each of its elements is also an element of \(A\). The elements of \(A\) are \(\emptyset\), \(\{\emptyset\}\), and \(1\). Options A, B, and C contain only elements from this list, so they are subsets of \(A\). Option D contains the element \(2\), but \(2\notin A\); therefore \(\{1,2\}\) is not a subset. Notice especially that \(\emptyset\) and \(\{\emptyset\}\) are different objects.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
