If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is \((A\cup B)^c\)?
Answer and explanation
Correct answer: \(\{5,6\}\)
First calculate the union: \(A\cup B=\{1,2,3,4\}\), because the union contains every element appearing in either set, with repeated elements written only once. The complement is taken relative to the universal set \(U\). Removing 1, 2, 3, and 4 from \(U\) leaves 5 and 6. Hence \((A\cup B)^c=\{5,6\}\), so option A is correct. The other choices either give the union, the intersection, or an incomplete complement.
Frequently asked questions
What is the correct answer to this question?
\(\{5,6\}\)
Why is this the correct answer?
First calculate the union: \(A\cup B=\{1,2,3,4\}\), because the union contains every element appearing in either set, with repeated elements written only once. The complement is taken relative to the universal set \(U\). Removing 1, 2, 3, and 4 from \(U\) leaves 5 and 6. Hence \((A\cup B)^c=\{5,6\}\), so option A is correct. The other choices either give the union, the intersection, or an incomplete complement.
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.
