If the universal set is U = ℝ and A = {x ∈ ℝ : x² = 4}, what is A'?
Answer and explanation
Correct answer: ℝ \ {-2, 2}
Solving x² = 4 over the real numbers gives x = −2 or x = 2. Thus A = {−2, 2}. The complement is always determined relative to the stated universal set. Since U = ℝ, remove these two elements from all real numbers: A' = ℝ \ {−2, 2}. Option B is A itself, while options C and D incorrectly ignore the two excluded real numbers.
Frequently asked questions
What is the correct answer to this question?
ℝ \ {-2, 2}
Why is this the correct answer?
Solving x² = 4 over the real numbers gives x = −2 or x = 2. Thus A = {−2, 2}. The complement is always determined relative to the stated universal set. Since U = ℝ, remove these two elements from all real numbers: A' = ℝ \ {−2, 2}. Option B is A itself, while options C and D incorrectly ignore the two excluded real numbers.
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.
