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

If A = {x : x ∈ ℤ, x² ≤ 4} and B = {-1, 0, 1, 3}, what is A ∩ B?

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Answer and explanation

Correct answer: {-1, 0, 1}

Because x is an integer and x² ≤ 4, we have |x| ≤ 2, so -2 ≤ x ≤ 2. Therefore A = {-2, -1, 0, 1, 2}. The intersection keeps only elements common to A and B. Comparing B = {-1, 0, 1, 3} with A, the common elements are -1, 0, and 1; 3 is not in A. Hence A ∩ B = {-1, 0, 1}, so option B is correct.

Tags

setsintersectionset-builder notationintegersOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{-1, 0, 1}

Why is this the correct answer?

Because x is an integer and x² ≤ 4, we have |x| ≤ 2, so -2 ≤ x ≤ 2. Therefore A = {-2, -1, 0, 1, 2}. The intersection keeps only elements common to A and B. Comparing B = {-1, 0, 1, 3} with A, the common elements are -1, 0, and 1; 3 is not in A. Hence A ∩ B = {-1, 0, 1}, so option B is correct.

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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