If the universal set is \(U=\mathbb{R}\), \(A=\{x\in\mathbb{R}:x\ne 0\}\), and \(B=\{x\in\mathbb{R}:x\ne 1\}\), what is \(A'\cup B'\)?
Answer and explanation
Correct answer: \(\{0,1\}\)
Complements are taken with respect to the universal set \(\mathbb{R}\). Set \(A\) contains every real number except 0, so \(A'=\{0\}\). Similarly, \(B\) contains every real number except 1, so \(B'=\{1\}\). Taking the union gives \(A'\cup B'=\{0\}\cup\{1\}=\{0,1\}\). Thus option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
\(\{0,1\}\)
Why is this the correct answer?
Complements are taken with respect to the universal set \(\mathbb{R}\). Set \(A\) contains every real number except 0, so \(A'=\{0\}\). Similarly, \(B\) contains every real number except 1, so \(B'=\{1\}\). Taking the union gives \(A'\cup B'=\{0\}\cup\{1\}=\{0,1\}\). Thus option A is the only correct answer.
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.
