If \(A \cup B' = B'\), which of the following conclusions is always true?
Answer and explanation
Correct answer: \(A \subseteq B'\)
For any sets \(X\) and \(Y\), the equality \(X\cup Y=Y\) holds exactly when every element of \(X\) is already an element of \(Y\). Thus \(X\subseteq Y\). Substituting \(X=A\) and \(Y=B'\) gives \(A\subseteq B'\). The other options either reverse the inclusion or assert equalities that do not follow from the given condition.
Frequently asked questions
What is the correct answer to this question?
\(A \subseteq B'\)
Why is this the correct answer?
For any sets \(X\) and \(Y\), the equality \(X\cup Y=Y\) holds exactly when every element of \(X\) is already an element of \(Y\). Thus \(X\subseteq Y\). Substituting \(X=A\) and \(Y=B'\) gives \(A\subseteq B'\). The other options either reverse the inclusion or assert equalities that do not follow from the given condition.
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.
