If \(A=\{1,2,3\}\), which is an element of \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: \(\{1,3\}\)
An element of \(\mathcal{P}(A)\) must be a subset of A. The set \(\{1,3\}\) contains only elements from A, so \(\{1,3\}\subseteq A\) and it belongs to \(\mathcal{P}(A)\). The object 1 is an element of A, not a subset by itself in this context; 4 is not in A, and \(\{\{4\}\}\) contains an element not belonging to A.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3\}\)
Why is this the correct answer?
An element of \(\mathcal{P}(A)\) must be a subset of A. The set \(\{1,3\}\) contains only elements from A, so \(\{1,3\}\subseteq A\) and it belongs to \(\mathcal{P}(A)\). The object 1 is an element of A, not a subset by itself in this context; 4 is not in A, and \(\{\{4\}\}\) contains an element not belonging to A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
