If \(A=\{x\in\mathbb{R}:x\ge 2\}\), \(B=\{x\in\mathbb{R}:x<6\}\), and \(C=\{x\in\mathbb{R}:x=4\}\), what is \((A\cap B)-C\)?
Answer and explanation
Correct answer: \([2,4)\cup(4,6)\)
The condition \(x\ge2\) gives the interval \([2,\infty)\), while \(x<6\) gives \((- infty,6)\). Their intersection is therefore \([2,6)\), including 2 but excluding 6. The set \(C\) contains only the number 4. Taking the difference \((A\cap B)-C\) removes 4 from \([2,6)\), leaving \([2,4)\cup(4,6)\). Thus, option A is correct; 4 is excluded from both resulting intervals.
Frequently asked questions
What is the correct answer to this question?
\([2,4)\cup(4,6)\)
Why is this the correct answer?
The condition \(x\ge2\) gives the interval \([2,\infty)\), while \(x<6\) gives \((- infty,6)\). Their intersection is therefore \([2,6)\), including 2 but excluding 6. The set \(C\) contains only the number 4. Taking the difference \((A\cap B)-C\) removes 4 from \([2,6)\), leaving \([2,4)\cup(4,6)\). Thus, option A is correct; 4 is excluded from both resulting intervals.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
