If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{x:x\in U,\ x<5\}\), what is \(A'\)?
Answer and explanation
Correct answer: \(\{5,6,7,8,9\}\)
The condition \(x<5\) selects the elements \(1,2,3,4\) from the universal set, so \(A=\{1,2,3,4\}\). The complement contains all elements of \(U\) that are not in this set. Therefore, \(A'=\{5,6,7,8,9\}\). Notice that 5 is included in the complement because the condition is strictly less than 5, not less than or equal to 5.
Frequently asked questions
What is the correct answer to this question?
\(\{5,6,7,8,9\}\)
Why is this the correct answer?
The condition \(x<5\) selects the elements \(1,2,3,4\) from the universal set, so \(A=\{1,2,3,4\}\). The complement contains all elements of \(U\) that are not in this set. Therefore, \(A'=\{5,6,7,8,9\}\). Notice that 5 is included in the complement because the condition is strictly less than 5, not less than or equal to 5.
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.
