If the universal set is U = ℝ and A = {x ∈ ℝ : |x − 2| < 5}, what is A'?
Answer and explanation
Correct answer: (−∞, −3] ∪ [7, ∞)
Solve the absolute-value inequality: |x − 2| < 5 means −5 < x − 2 < 5. Adding 2 gives −3 < x < 7, so A = (−3, 7). Since the complement is taken in U = ℝ, it contains every real number outside this open interval. The boundary points −3 and 7 are included in the complement, giving A' = (−∞, −3] ∪ [7, ∞). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
(−∞, −3] ∪ [7, ∞)
Why is this the correct answer?
Solve the absolute-value inequality: |x − 2| < 5 means −5 < x − 2 < 5. Adding 2 gives −3 < x < 7, so A = (−3, 7). Since the complement is taken in U = ℝ, it contains every real number outside this open interval. The boundary points −3 and 7 are included in the complement, giving A' = (−∞, −3] ∪ [7, ∞). 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.
