If A = {x ∈ Z : |x − 2| < 2} and B = {1, 2, 3}, which statement is correct?
Answer and explanation
Correct answer: A = B
For an absolute-value inequality, |x − 2| < 2 is equivalent to −2 < x − 2 < 2. Adding 2 throughout gives 0 < x < 4. Since x must be an integer, the only possible values are 1, 2, and 3. Thus A = {1, 2, 3}, which is exactly B. Therefore A = B is correct; neither set is a proper subset of the other, and their intersection is not empty.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
For an absolute-value inequality, |x − 2| < 2 is equivalent to −2 < x − 2 < 2. Adding 2 throughout gives 0 < x < 4. Since x must be an integer, the only possible values are 1, 2, and 3. Thus A = {1, 2, 3}, which is exactly B. Therefore A = B is correct; neither set is a proper subset of the other, and their intersection is not empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
