If \(A=\{3,6,9\}\), which statement is correct about \(\{3,9\}\)?
Answer and explanation
Correct answer: \(\{3,9\}\in\mathcal{P}(A)\)
The set \(\{3,9\}\) contains the elements 3 and 9, and both are elements of \(A\). Therefore, \(\{3,9\}\subseteq A\). The power set \(\mathcal{P}(A)\) contains every subset of \(A\), so \(\{3,9\}\) is an element of \(\mathcal{P}(A)\). Option A is false because \(A\) contains numbers, not the set \(\{3,9\}\); option C is false because 6 is missing; option D contradicts the subset relation.
Frequently asked questions
What is the correct answer to this question?
\(\{3,9\}\in\mathcal{P}(A)\)
Why is this the correct answer?
The set \(\{3,9\}\) contains the elements 3 and 9, and both are elements of \(A\). Therefore, \(\{3,9\}\subseteq A\). The power set \(\mathcal{P}(A)\) contains every subset of \(A\), so \(\{3,9\}\) is an element of \(\mathcal{P}(A)\). Option A is false because \(A\) contains numbers, not the set \(\{3,9\}\); option C is false because 6 is missing; option D contradicts the subset relation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
