If \(\{m,n\}\in\mathcal{P}(A)\), which statement is definitely true?
Answer and explanation
Correct answer: \(m\in A\) and \(n\in A\)
By definition, \(\mathcal{P}(A)\) contains exactly the subsets of \(A\). Thus \(\{m,n\}\in\mathcal{P}(A)\) means \(\{m,n\}\subseteq A\). Every element of this subset must belong to \(A\), so both \(m\in A\) and \(n\in A\). The statement does not imply that \(A\) has no other elements, so option C is not necessary. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(m\in A\) and \(n\in A\)
Why is this the correct answer?
By definition, \(\mathcal{P}(A)\) contains exactly the subsets of \(A\). Thus \(\{m,n\}\in\mathcal{P}(A)\) means \(\{m,n\}\subseteq A\). Every element of this subset must belong to \(A\), so both \(m\in A\) and \(n\in A\). The statement does not imply that \(A\) has no other elements, so option C is not necessary. 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.
