For a universal set \(U\), what is \(A\cup A'\) equal to?
Answer and explanation
Correct answer: \(U\)
The complement \(A'\) consists of all elements of the universal set \(U\) that are not in \(A\). Therefore, every element of \(U\) lies either in \(A\) or in \(A'\), and hence belongs to their union. Consequently, \(A\cup A'=U\). This is one of De Morgan’s basic complement laws; in contrast, \(A\cap A'=\varnothing\).
Frequently asked questions
What is the correct answer to this question?
\(U\)
Why is this the correct answer?
The complement \(A'\) consists of all elements of the universal set \(U\) that are not in \(A\). Therefore, every element of \(U\) lies either in \(A\) or in \(A'\), and hence belongs to their union. Consequently, \(A\cup A'=U\). This is one of De Morgan’s basic complement laws; in contrast, \(A\cap A'=\varnothing\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
