If the universal set is U = ℝ and A = {x : x² = 4}, what does A′ represent?
Answer and explanation
Correct answer: All real numbers except −2 and 2
Solving x² = 4 gives x = 2 or x = −2, so A = {−2, 2}. Because the universal set is the set of all real numbers, A′ consists of every real number that is not −2 and not 2. It can be written as ℝ \ {−2,2}, or equivalently as all real numbers except −2 and 2. It is not limited to integers, and it is certainly not empty because infinitely many other real numbers remain.
Frequently asked questions
What is the correct answer to this question?
All real numbers except −2 and 2
Why is this the correct answer?
Solving x² = 4 gives x = 2 or x = −2, so A = {−2, 2}. Because the universal set is the set of all real numbers, A′ consists of every real number that is not −2 and not 2. It can be written as ℝ \ {−2,2}, or equivalently as all real numbers except −2 and 2. It is not limited to integers, and it is certainly not empty because infinitely many other real numbers remain.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
