If \(A\subseteq C\) and \(B\subseteq C\), what is \((A\cup B)\setminus C\)?
Answer and explanation
Correct answer: \(\varnothing\)
Because \(A\subseteq C\), every element of \(A\) belongs to \(C\). Similarly, every element of \(B\) belongs to \(C\). Therefore every element of \(A\cup B\) is also in \(C\). Set difference removes elements that are in \(C\), so no element remains: \((A\cup B)\setminus C=\varnothing\). Thus option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
Because \(A\subseteq C\), every element of \(A\) belongs to \(C\). Similarly, every element of \(B\) belongs to \(C\). Therefore every element of \(A\cup B\) is also in \(C\). Set difference removes elements that are in \(C\), so no element remains: \((A\cup B)\setminus C=\varnothing\). Thus option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
