If \(A=\{100,200,300\}\), why is \(A\) itself an element of \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: because \(A\subseteq A\)
The power set \(\mathcal{P}(A)\) is defined as the set of all subsets of \(A\). Every set is a subset of itself because each element of the set is certainly contained in that same set; thus \(A\subseteq A\). Consequently, \(A\) is one of the subsets collected in \(\mathcal{P}(A)\), so \(A\in\mathcal{P}(A)\). The other options confuse set membership with subset relation or give false conditions.
Frequently asked questions
What is the correct answer to this question?
because \(A\subseteq A\)
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) is defined as the set of all subsets of \(A\). Every set is a subset of itself because each element of the set is certainly contained in that same set; thus \(A\subseteq A\). Consequently, \(A\) is one of the subsets collected in \(\mathcal{P}(A)\), so \(A\in\mathcal{P}(A)\). The other options confuse set membership with subset relation or give false conditions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
