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

If A = {x ∈ R | x² − 9 = 0} and B = {x ∈ R | x² − 6x + 9 = 0}, what is A ∪ B?

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Answer and explanation

Correct answer: {−3, 3}

Solve the first equation: x² − 9 = (x − 3)(x + 3) = 0, so A = {−3, 3}. The second equation is x² − 6x + 9 = (x − 3)² = 0, so B = {3}. A union contains every distinct element appearing in either set; because 3 is repeated, it is written only once. Hence A ∪ B = {−3, 3}.

Tags

setsunionset-builder notationquadratic equationsOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{−3, 3}

Why is this the correct answer?

Solve the first equation: x² − 9 = (x − 3)(x + 3) = 0, so A = {−3, 3}. The second equation is x² − 6x + 9 = (x − 3)² = 0, so B = {3}. A union contains every distinct element appearing in either set; because 3 is repeated, it is written only once. Hence A ∪ B = {−3, 3}.

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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