If \(A=\{2,4,6,8\}\), which of the following is not an element of \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: \(\{2,10\}\)
The power set \(\mathcal{P}(A)\) contains exactly the subsets of \(A\). A candidate set belongs to \(\mathcal{P}(A)\) only when every one of its elements belongs to \(A\). Both 2 and 8 are in \(A\), so \(\{2,8\}\) qualifies; similarly, \(\{4,6\}\) qualifies. The empty set is a subset of every set. However, 10 is not in \(A\), so \(\{2,10\}\) is not a subset and cannot belong to the power set.
Frequently asked questions
What is the correct answer to this question?
\(\{2,10\}\)
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) contains exactly the subsets of \(A\). A candidate set belongs to \(\mathcal{P}(A)\) only when every one of its elements belongs to \(A\). Both 2 and 8 are in \(A\), so \(\{2,8\}\) qualifies; similarly, \(\{4,6\}\) qualifies. The empty set is a subset of every set. However, 10 is not in \(A\), so \(\{2,10\}\) is not a subset and cannot belong to the power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
