If \(A=\{1,2,3\}\) and \(B=\{2,3,4\}\), which element is in \(A\cup B\) but not in \(A\cap B\)?
Answer and explanation
Correct answer: \(1\)
The union contains every element appearing in either set, so \(A\cup B=\{1,2,3,4\}\). The intersection contains only elements common to both sets, so \(A\cap B=\{2,3\}\). Element 1 belongs to A and therefore to the union, but it does not belong to B and therefore is not in the intersection. Thus option A is correct. Elements 2 and 3 are in both sets, so they belong to the intersection and cannot satisfy the condition.
Frequently asked questions
What is the correct answer to this question?
\(1\)
Why is this the correct answer?
The union contains every element appearing in either set, so \(A\cup B=\{1,2,3,4\}\). The intersection contains only elements common to both sets, so \(A\cap B=\{2,3\}\). Element 1 belongs to A and therefore to the union, but it does not belong to B and therefore is not in the intersection. Thus option A is correct. Elements 2 and 3 are in both sets, so they belong to the intersection and cannot satisfy the condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
