Let A = {x ∈ Z : |x − 2| < 2}. Which of the following is a proper subset of A?
Answer and explanation
Correct answer: {1, 3}
Solve the absolute-value inequality: |x − 2| < 2 gives −2 < x − 2 < 2. Adding 2 throughout yields 0 < x < 4. Since x must be an integer, A = {1, 2, 3}. The set {1, 3} contains only elements of A, so it is a subset of A, but it does not contain 2 and therefore is not equal to A. Hence it is a proper subset. Option A equals A, while C and D contain elements not belonging to A.
Frequently asked questions
What is the correct answer to this question?
{1, 3}
Why is this the correct answer?
Solve the absolute-value inequality: |x − 2| < 2 gives −2 < x − 2 < 2. Adding 2 throughout yields 0 < x < 4. Since x must be an integer, A = {1, 2, 3}. The set {1, 3} contains only elements of A, so it is a subset of A, but it does not contain 2 and therefore is not equal to A. Hence it is a proper subset. Option A equals A, while C and D contain elements not belonging to A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
