If \(U=\{1,2,3,\ldots,16\}\), \(A=\{1,4,9,16\}\), and \(B=\{2,4,6,8,10,12,14,16\}\), what is \((A\cup B)^c\)?
Answer and explanation
Correct answer: \(\{3,5,7,11,13,15\}\)
First combine the sets: \(A\cup B=\{1,2,4,6,8,9,10,12,14,16\}\). The complement contains every element of U not appearing in this union. Checking the integers 1 through 16 leaves \(\{3,5,7,11,13,15\}\). Therefore option A is correct. Notice that repeated elements such as 4 and 16 are written only once in a union.
Frequently asked questions
What is the correct answer to this question?
\(\{3,5,7,11,13,15\}\)
Why is this the correct answer?
First combine the sets: \(A\cup B=\{1,2,4,6,8,9,10,12,14,16\}\). The complement contains every element of U not appearing in this union. Checking the integers 1 through 16 leaves \(\{3,5,7,11,13,15\}\). Therefore option A is correct. Notice that repeated elements such as 4 and 16 are written only once in a union.
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.
