For a universal set \(U\), what is \(A\cap A'\) equal to?
Answer and explanation
Correct answer: \(\varnothing\)
By definition, \(A'\) contains exactly those elements of \(U\) that are not in \(A\). Thus no element can belong to both \(A\) and \(A'\) simultaneously. Their common part is therefore empty, giving \(A\cap A'=\varnothing\). This conclusion remains valid for every set \(A\) relative to the same universal set \(U\), including when \(A\) itself is empty or equal to \(U\).
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
By definition, \(A'\) contains exactly those elements of \(U\) that are not in \(A\). Thus no element can belong to both \(A\) and \(A'\) simultaneously. Their common part is therefore empty, giving \(A\cap A'=\varnothing\). This conclusion remains valid for every set \(A\) relative to the same universal set \(U\), including when \(A\) itself is empty or equal to \(U\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
