If \(A=[1,10]\), \(B=[3,7]\), and \(C=(5,12)\), what is \(A\setminus(B\cup C)\)?
Answer and explanation
Correct answer: \([1,3)\)
The union \(B\cup C\) begins at 3 because 3 is included in \(B\). The intervals overlap from 5 onward, and \(C\) continues to values just below 12, so \(B\cup C=[3,12)\). Taking the elements of \(A=[1,10]\) that are not in this union leaves the interval from 1 through values less than 3: \([1,3)\). The point 1 is included, while 3 is excluded because it belongs to \(B\).
Frequently asked questions
What is the correct answer to this question?
\([1,3)\)
Why is this the correct answer?
The union \(B\cup C\) begins at 3 because 3 is included in \(B\). The intervals overlap from 5 onward, and \(C\) continues to values just below 12, so \(B\cup C=[3,12)\). Taking the elements of \(A=[1,10]\) that are not in this union leaves the interval from 1 through values less than 3: \([1,3)\). The point 1 is included, while 3 is excluded because it belongs to \(B\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
