If \(A=\{p,q,r\}\), what is \(A\setminus A\)?
Answer and explanation
Correct answer: \(\varnothing\)
The difference \(A\setminus A\) consists of elements that belong to the first copy of \(A\) but do not belong to the second copy. Since both sets are identical, every element \(p\), \(q\), and \(r\) is removed. No element can remain in one copy while being absent from the other, so \(A\setminus A=\varnothing\). This is a general identity for every set.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The difference \(A\setminus A\) consists of elements that belong to the first copy of \(A\) but do not belong to the second copy. Since both sets are identical, every element \(p\), \(q\), and \(r\) is removed. No element can remain in one copy while being absent from the other, so \(A\setminus A=\varnothing\). This is a general identity for every set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
