If U={0,1,2,3,4,5,6,7,8,9} and A={x∈U:x^2<25}, what is the complement A' with respect to U?
Answer and explanation
Correct answer: {5,6,7,8,9}
Because U contains only nonnegative integers, the condition x^2<25 is satisfied by x=0,1,2,3,4. The value x=5 is excluded because 5^2=25, and the inequality is strict. Thus A={0,1,2,3,4}. The relative complement contains the elements of U outside A, namely A'=U−A={5,6,7,8,9}. Therefore, option A is correct. Checking the boundary value 5 prevents confusing <25 with ≤25.
Frequently asked questions
What is the correct answer to this question?
{5,6,7,8,9}
Why is this the correct answer?
Because U contains only nonnegative integers, the condition x^2<25 is satisfied by x=0,1,2,3,4. The value x=5 is excluded because 5^2=25, and the inequality is strict. Thus A={0,1,2,3,4}. The relative complement contains the elements of U outside A, namely A'=U−A={5,6,7,8,9}. Therefore, option A is correct. Checking the boundary value 5 prevents confusing <25 with ≤25.
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.
