If \(A=\{10,20,30\}\), which of the following must be an element of \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: \{20\}
The power set \(\mathcal{P}(A)\) contains every subset of \(A\), including the empty set, singleton subsets, two-element subsets, and \(A\) itself. Since 20 belongs to \(A\), the singleton set \(\{20\}\) is a subset of \(A\), and therefore \(\{20\}\in\mathcal{P}(A)\). The number 40 is not in \(A\), so \(\{40\}\) is not a subset of \(A\).
Frequently asked questions
What is the correct answer to this question?
\{20\}
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) contains every subset of \(A\), including the empty set, singleton subsets, two-element subsets, and \(A\) itself. Since 20 belongs to \(A\), the singleton set \(\{20\}\) is a subset of \(A\), and therefore \(\{20\}\in\mathcal{P}(A)\). The number 40 is not in \(A\), so \(\{40\}\) 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.
