If \(A=\{d,e,f\}\), why is \(\emptyset\) in \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: because \(\emptyset\subseteq A\)
The power set \(\mathcal{P}(A)\) consists of every subset of \(A\). The empty set has no elements, so it cannot contain any element outside \(A\); for this reason, \(\emptyset\subseteq A\) is true for every set \(A\). Hence \(\emptyset\) is one of the subsets included in \(\mathcal{P}(A)\). It is not equal to the nonempty set \(A\), nor does it necessarily belong to \(A\) as an element.
Frequently asked questions
What is the correct answer to this question?
because \(\emptyset\subseteq A\)
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) consists of every subset of \(A\). The empty set has no elements, so it cannot contain any element outside \(A\); for this reason, \(\emptyset\subseteq A\) is true for every set \(A\). Hence \(\emptyset\) is one of the subsets included in \(\mathcal{P}(A)\). It is not equal to the nonempty set \(A\), nor does it necessarily belong to \(A\) as an element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
