If \(A=\{1,2,3\}\), which statement about \(\{1,3\}\) in \(P(A)\) is correct?
Answer and explanation
Correct answer: \(\{1,3\}\in P(A)\)
The power set \(P(A)\) is the set of all subsets of \(A\). Since both 1 and 3 belong to \(A\), the set \(\{1,3\}\) is a subset of \(A\). Every subset of \(A\) is an element of \(P(A)\), so \(\{1,3\}\in P(A)\). Notice the distinction: 1 and 3 are elements of \(A\), while the set \(\{1,3\}\) is an element of the power set. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3\}\in P(A)\)
Why is this the correct answer?
The power set \(P(A)\) is the set of all subsets of \(A\). Since both 1 and 3 belong to \(A\), the set \(\{1,3\}\) is a subset of \(A\). Every subset of \(A\) is an element of \(P(A)\), so \(\{1,3\}\in P(A)\). Notice the distinction: 1 and 3 are elements of \(A\), while the set \(\{1,3\}\) is an element of the power set. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
