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

If A = {x ∈ ℤ : |2x − 1| < 4} and B = {−1, 0, 1, 2}, which conclusion is correct?

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Answer and explanation

Correct answer: A = B

We solve the absolute-value inequality first: |2x − 1| < 4 implies −4 < 2x − 1 < 4. Adding 1 and dividing by 2 gives −3/2 < x < 5/2. Since x must be an integer, the possible values are −1, 0, 1, and 2. Therefore A = {−1, 0, 1, 2}, which is exactly the set B. Hence the correct conclusion is A = B.

Tags

setsequal-setsabsolute-valueintegersfinite-setsThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematics

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

We solve the absolute-value inequality first: |2x − 1| < 4 implies −4 < 2x − 1 < 4. Adding 1 and dividing by 2 gives −3/2 < x < 5/2. Since x must be an integer, the possible values are −1, 0, 1, and 2. Therefore A = {−1, 0, 1, 2}, which is exactly the set B. Hence the correct conclusion is 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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