If \(U=\mathbb{R}\) and \(A=\{x:x^2-5x+6=0\}\), which is the correct description of \(A'\)?
Answer and explanation
Correct answer: \(\mathbb{R}\setminus\{2,3\}\)
Factor the quadratic as \(x^2-5x+6=(x-2)(x-3)\). Therefore, the solutions are \(x=2\) and \(x=3\), so \(A=\{2,3\}\). Since the universal set is all real numbers, the complement contains every real number except 2 and 3. Hence \(A'=\mathbb{R}\setminus\{2,3\}\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(\mathbb{R}\setminus\{2,3\}\)
Why is this the correct answer?
Factor the quadratic as \(x^2-5x+6=(x-2)(x-3)\). Therefore, the solutions are \(x=2\) and \(x=3\), so \(A=\{2,3\}\). Since the universal set is all real numbers, the complement contains every real number except 2 and 3. Hence \(A'=\mathbb{R}\setminus\{2,3\}\), making option A 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.
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