If U = R and A = {x : |x − 3| < 5}, what is A'?
Answer and explanation
Correct answer: (-∞, -2] ∪ [8, ∞)
Solve the absolute-value inequality: |x − 3| < 5 means −5 < x − 3 < 5. Adding 3 throughout gives −2 < x < 8, so A = (−2, 8). Since the universal set is all real numbers, the complement contains the endpoints and all values outside the interval: A' = (−∞, −2] ∪ [8, ∞). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
(-∞, -2] ∪ [8, ∞)
Why is this the correct answer?
Solve the absolute-value inequality: |x − 3| < 5 means −5 < x − 3 < 5. Adding 3 throughout gives −2 < x < 8, so A = (−2, 8). Since the universal set is all real numbers, the complement contains the endpoints and all values outside the interval: A' = (−∞, −2] ∪ [8, ∞). Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
