If \(A=\{0,1,2\}\), which of the following is not a subset of A?
Answer and explanation
Correct answer: \(\{\varnothing\}\)
A set C is a subset of A when every element of C is also an element of A. The empty set is a subset of every set, so option A qualifies. Both 0 and 2 are in A, making option B a subset, and 1 is in A, making option C a subset. In option D, the only element is the empty set \(\varnothing\), not the number 0. Since \(\varnothing\notin A\), the set \(\{\varnothing\}\) is not a subset of A.
Frequently asked questions
What is the correct answer to this question?
\(\{\varnothing\}\)
Why is this the correct answer?
A set C is a subset of A when every element of C is also an element of A. The empty set is a subset of every set, so option A qualifies. Both 0 and 2 are in A, making option B a subset, and 1 is in A, making option C a subset. In option D, the only element is the empty set \(\varnothing\), not the number 0. Since \(\varnothing\notin A\), the set \(\{\varnothing\}\) is not a subset of A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
