If \(A'\cap B'=A'\), which of the following conclusions is always true?
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Answer and explanation
Correct answer: \(A'\subseteq B'\)
The identity \(A'\cap B'=A'\) says that intersecting \(A'\) with \(B'\) removes nothing from \(A'\). This can happen only when every element of \(A'\) is already in \(B'\). Therefore \(A'\subseteq B'\). Taking complements would equivalently give \(B\subseteq A\), not necessarily \(A\subseteq B\).
Frequently asked questions
What is the correct answer to this question?
\(A'\subseteq B'\)
Why is this the correct answer?
The identity \(A'\cap B'=A'\) says that intersecting \(A'\) with \(B'\) removes nothing from \(A'\). This can happen only when every element of \(A'\) is already in \(B'\). Therefore \(A'\subseteq B'\). Taking complements would equivalently give \(B\subseteq A\), not necessarily \(A\subseteq B\).
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.
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