If \(A\subseteq B\), which relation between their complements is correct?
Answer and explanation
Correct answer: \(B^c\subseteq A^c\)
If every element of \(A\) is also in \(B\), then any element outside \(B\) must certainly be outside \(A\). Thus, the elements of \(B^c\) are a subset of the elements of \(A^c\), giving \(B^c\subseteq A^c\). Complementation reverses the direction of a subset relation; this is called order reversal.
Frequently asked questions
What is the correct answer to this question?
\(B^c\subseteq A^c\)
Why is this the correct answer?
If every element of \(A\) is also in \(B\), then any element outside \(B\) must certainly be outside \(A\). Thus, the elements of \(B^c\) are a subset of the elements of \(A^c\), giving \(B^c\subseteq A^c\). Complementation reverses the direction of a subset relation; this is called order reversal.
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.
