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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 4

If A = {x : x ∈ Z, (x − 1)(x − 2)(x − 3) = 0} and B = {3, 2, 1, 2}, which conclusion is correct?

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Answer and explanation

Correct answer: A = B

A product is zero when at least one factor is zero. Hence x − 1 = 0, x − 2 = 0, or x − 3 = 0, giving A = {1, 2, 3}. In set notation, repetition does not create a new element, so B = {3, 2, 1, 2} is also {1, 2, 3}. Order and repeated writing do not affect set equality; therefore A = B.

Tags

setsequal setsrepeated elementszero product propertyThe Empty SetFinite and Infinite Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

A product is zero when at least one factor is zero. Hence x − 1 = 0, x − 2 = 0, or x − 3 = 0, giving A = {1, 2, 3}. In set notation, repetition does not create a new element, so B = {3, 2, 1, 2} is also {1, 2, 3}. Order and repeated writing do not affect set equality; therefore A = B.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.

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