If \(A=\{p,q,r,s\}\) and \(B=\{p,r\}\), which subsets of B are also subsets of A?
Answer and explanation
Correct answer: All subsets of B
Because both p and r belong to A, every element of B belongs to A; hence \(B\subseteq A\). The subsets of B are \(\varnothing\), \(\{p\}\), \(\{r\}\), and \(\{p,r\}\). Each of these contains only elements from A, so each is also a subset of A. This is the transitive property of inclusion: if \(C\subseteq B\) and \(B\subseteq A\), then \(C\subseteq A\). Therefore all subsets of B satisfy the requirement.
Frequently asked questions
What is the correct answer to this question?
All subsets of B
Why is this the correct answer?
Because both p and r belong to A, every element of B belongs to A; hence \(B\subseteq A\). The subsets of B are \(\varnothing\), \(\{p\}\), \(\{r\}\), and \(\{p,r\}\). Each of these contains only elements from A, so each is also a subset of A. This is the transitive property of inclusion: if \(C\subseteq B\) and \(B\subseteq A\), then \(C\subseteq A\). Therefore all subsets of B satisfy the requirement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
