If \(A\subset B\) and \(B\subset C\), which statement about \(A\) and \(C\) is correct?
Answer and explanation
Correct answer: \(A\subset C\)
Because \(A\subset B\), every element of A belongs to B, and because \(B\subset C\), every element of B belongs to C. Therefore \(A\subseteq C\). Moreover, A cannot equal C: if A equalled C, then the chain \(A\subset B\subset C=A\) would force B to be simultaneously larger than A and contained in A, which is impossible. Thus \(A\subset C\) is proper.
Frequently asked questions
What is the correct answer to this question?
\(A\subset C\)
Why is this the correct answer?
Because \(A\subset B\), every element of A belongs to B, and because \(B\subset C\), every element of B belongs to C. Therefore \(A\subseteq C\). Moreover, A cannot equal C: if A equalled C, then the chain \(A\subset B\subset C=A\) would force B to be simultaneously larger than A and contained in A, which is impossible. Thus \(A\subset C\) is proper.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
