If \(A\subseteq U\), what is \(A'\cap A\)?
Answer and explanation
Correct answer: \(\emptyset\)
The complement \(A'\) contains the elements of the universal set \(U\) that are not in \(A\). The intersection \(A'\cap A\) would require an element to be in \(A\) and not in \(A\) at the same time, which is impossible. Therefore, the two sets are disjoint and \(A'\cap A=\emptyset\). This is one of the fundamental complement identities; the related union identity is \(A\cup A'=U\). Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
\(\emptyset\)
Why is this the correct answer?
The complement \(A'\) contains the elements of the universal set \(U\) that are not in \(A\). The intersection \(A'\cap A\) would require an element to be in \(A\) and not in \(A\) at the same time, which is impossible. Therefore, the two sets are disjoint and \(A'\cap A=\emptyset\). This is one of the fundamental complement identities; the related union identity is \(A\cup A'=U\). Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
