If \(A\cup B=A\), what is the value of \(B\setminus A\)?
Answer and explanation
Correct answer: \(\varnothing\)
The equality \(A\cup B=A\) means that adding every element of \(B\) to \(A\) does not produce any new element. Therefore, every element of \(B\) is already an element of \(A\), so \(B\subseteq A\). The difference \(B\setminus A\) contains elements that belong to \(B\) but do not belong to \(A\). Since no such element exists, \(B\setminus A=\varnothing\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The equality \(A\cup B=A\) means that adding every element of \(B\) to \(A\) does not produce any new element. Therefore, every element of \(B\) is already an element of \(A\), so \(B\subseteq A\). The difference \(B\setminus A\) contains elements that belong to \(B\) but do not belong to \(A\). Since no such element exists, \(B\setminus A=\varnothing\). Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
