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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 16

If A = [−4, 2) ∪ (5, 9] and B = (−1, 6], what is A \ B?

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Answer and explanation

Correct answer: [−4, −1] ∪ (6, 9]

To find A \ B, retain points of A that do not belong to B. From [−4, 2), remove (−1, 2), but −1 remains because B is open at −1; this leaves [−4, −1]. From (5, 9], remove (5, 6], including 6 because B contains 6; this leaves (6, 9]. Hence A \ B = [−4, −1] ∪ (6, 9].

Tags

setsintervalsset-differenceendpoint-notationOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

[−4, −1] ∪ (6, 9]

Why is this the correct answer?

To find A \ B, retain points of A that do not belong to B. From [−4, 2), remove (−1, 2), but −1 remains because B is open at −1; this leaves [−4, −1]. From (5, 9], remove (5, 6], including 6 because B contains 6; this leaves (6, 9]. Hence A \ B = [−4, −1] ∪ (6, 9].

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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