Let \(U=\{1,2,3,\ldots,20\}\) and \(A=\{x:x\in U\text{ and }x\text{ is prime}\}\). What is \(A'\), the complement of \(A\) with respect to \(U\)?
Answer and explanation
Correct answer: \(\{1,4,6,8,9,10,12,14,15,16,18,20\}\)
The prime numbers in \(U\) are \(2,3,5,7,11,13,17,19\). The complement contains every element of the stated universal set that is not prime. Thus it contains 1 and all composite numbers from 4 to 20: \(A'=\{1,4,6,8,9,10,12,14,15,16,18,20\}\). Remember that 1 is neither prime nor composite, but it is still in the complement.
Frequently asked questions
What is the correct answer to this question?
\(\{1,4,6,8,9,10,12,14,15,16,18,20\}\)
Why is this the correct answer?
The prime numbers in \(U\) are \(2,3,5,7,11,13,17,19\). The complement contains every element of the stated universal set that is not prime. Thus it contains 1 and all composite numbers from 4 to 20: \(A'=\{1,4,6,8,9,10,12,14,15,16,18,20\}\). Remember that 1 is neither prime nor composite, but it is still in the 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.
