For subsets \(A\) and \(B\) of a universal set \(U\), if \(A\subseteq B\), which relation between their complements is always true?
Answer and explanation
Correct answer: \(B'\subseteq A'\)
Because \(A\subseteq B\), every element of \(A\) is also an element of \(B\). Now take any element \(x\in B'\). It is not in \(B\); therefore it cannot be in the smaller set \(A\), so \(x\in A'\). Hence every element of \(B'\) belongs to \(A'\), giving \(B'\subseteq A'\). Complementation reverses inclusion.
Frequently asked questions
What is the correct answer to this question?
\(B'\subseteq A'\)
Why is this the correct answer?
Because \(A\subseteq B\), every element of \(A\) is also an element of \(B\). Now take any element \(x\in B'\). It is not in \(B\); therefore it cannot be in the smaller set \(A\), so \(x\in A'\). Hence every element of \(B'\) belongs to \(A'\), giving \(B'\subseteq A'\). Complementation reverses inclusion.
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.
