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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 17

If A = {x ∈ R : 1 ≤ x ≤ 9} and B = {x ∈ R : 3 < x < 7}, what is A − B?

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Answer and explanation

Correct answer: [1, 3] ∪ [7, 9]

A is the closed interval [1, 9], while B is the open interval (3, 7). To find A − B, remove every real number strictly between 3 and 7 from A. The endpoints 3 and 7 are not elements of B because B uses strict inequalities, so they remain. The result is [1, 3] ∪ [7, 9].

Tags

setsset-differenceinterval-notationreal-numbersoperations-on-setsOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

[1, 3] ∪ [7, 9]

Why is this the correct answer?

A is the closed interval [1, 9], while B is the open interval (3, 7). To find A − B, remove every real number strictly between 3 and 7 from A. The endpoints 3 and 7 are not elements of B because B uses strict inequalities, so they remain. The result is [1, 3] ∪ [7, 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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