If \(A\subseteq B'\), which of the following relations is always true?
Answer and explanation
Correct answer: \(A\cap B=\varnothing\)
The statement \(A\subseteq B'\) says that every element of \(A\) lies outside \(B\). Consequently, no element can belong to both sets, so \(A\cap B=\varnothing\). The union need not be empty: both sets may contain many elements while remaining disjoint. Also, the condition does not imply that \(B\subseteq A\) or that the two complements are equal.
Frequently asked questions
What is the correct answer to this question?
\(A\cap B=\varnothing\)
Why is this the correct answer?
The statement \(A\subseteq B'\) says that every element of \(A\) lies outside \(B\). Consequently, no element can belong to both sets, so \(A\cap B=\varnothing\). The union need not be empty: both sets may contain many elements while remaining disjoint. Also, the condition does not imply that \(B\subseteq A\) or that the two complements are equal.
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.
