Which of the following is an element of the power set \(P(A)\) of \(A=\{1,2,3\}\)?
Answer and explanation
Correct answer: \(\{2,3\}\)
The elements of \(P(A)\) are exactly the subsets of A. Option B, \(\{2,3\}\), is a subset because both 2 and 3 belong to A; therefore it is an element of \(P(A)\). Option A is only the number 2, an element of A but not a subset of A. Option C is not a subset because 4 is absent from A. Option D contains the set \(\{1\}\) as its element, rather than the number 1, so it is not a subset of A. The distinction between membership and subset notation is essential.
Frequently asked questions
What is the correct answer to this question?
\(\{2,3\}\)
Why is this the correct answer?
The elements of \(P(A)\) are exactly the subsets of A. Option B, \(\{2,3\}\), is a subset because both 2 and 3 belong to A; therefore it is an element of \(P(A)\). Option A is only the number 2, an element of A but not a subset of A. Option C is not a subset because 4 is absent from A. Option D contains the set \(\{1\}\) as its element, rather than the number 1, so it is not a subset of A. The distinction between membership and subset notation is essential.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
