If \(A=\{7,14,21\}\), which of 7 and \(\{7\}\) is an element of \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: only \(\{7\}\)
The power set \(\mathcal{P}(A)\) contains all subsets of \(A\), not all individual elements of \(A\). Since 7 belongs to \(A\), the singleton \(\{7\}\) is a subset of \(A\), and therefore \(\{7\}\in\mathcal{P}(A)\). The number 7 itself is an element of \(A\), but it is not a subset of \(A\), so it is not an element of the power set. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
only \(\{7\}\)
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) contains all subsets of \(A\), not all individual elements of \(A\). Since 7 belongs to \(A\), the singleton \(\{7\}\) is a subset of \(A\), and therefore \(\{7\}\in\mathcal{P}(A)\). The number 7 itself is an element of \(A\), but it is not a subset of \(A\), so it is not an element of the power set. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
