If \(A\cap B=\varnothing\), which statement about \(B\) must be true?
Answer and explanation
Correct answer: \(B\subseteq A'\)
The condition \(A\cap B=\varnothing\) means that no element is common to both \(A\) and \(B\). Therefore, every element of \(B\) lies outside \(A\). By the definition of complement, all such elements belong to \(A'\), so \(B\subseteq A'\) must hold. The other statements need not always be true: \(B\) may be smaller than \(A'\), and the union need not equal \(U\).
Frequently asked questions
What is the correct answer to this question?
\(B\subseteq A'\)
Why is this the correct answer?
The condition \(A\cap B=\varnothing\) means that no element is common to both \(A\) and \(B\). Therefore, every element of \(B\) lies outside \(A\). By the definition of complement, all such elements belong to \(A'\), so \(B\subseteq A'\) must hold. The other statements need not always be true: \(B\) may be smaller than \(A'\), and the union need not equal \(U\).
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.
