If \(A=\{x\in\mathbb{R}\mid 0\le x<5\}\) and \(B=\{x\in\mathbb{R}\mid 3<x\le 8\}\), what is \((A\cup B)\setminus(A\cap B)\)?
Answer and explanation
Correct answer: \([0,3]\cup[5,8]\)
The first interval is \(A=[0,5)\), while the second is \(B=(3,8]\). Their union covers every real number from 0 through 8, so \(A\cup B=[0,8]\). Their intersection consists of numbers common to both, namely \((3,5)\). Removing this common part from the union leaves the numbers in exactly one set: \([0,3]\cup[5,8]\). The endpoints 3 and 5 are included because 3 belongs to A but not B, and 5 belongs to B but not A.
Frequently asked questions
What is the correct answer to this question?
\([0,3]\cup[5,8]\)
Why is this the correct answer?
The first interval is \(A=[0,5)\), while the second is \(B=(3,8]\). Their union covers every real number from 0 through 8, so \(A\cup B=[0,8]\). Their intersection consists of numbers common to both, namely \((3,5)\). Removing this common part from the union leaves the numbers in exactly one set: \([0,3]\cup[5,8]\). The endpoints 3 and 5 are included because 3 belongs to A but not B, and 5 belongs to B but not A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
