If the universal set \(U=\{x\in\mathbb Z\mid -5\le x\le 5\}\) and \(A=\{x\in\mathbb Z\mid x^2<9\}\), what is the complement \(A^c\) of A?
Answer and explanation
Correct answer: \(\{-5,-4,-3,3,4,5\}\)
The condition \(x^2<9\) means \(-3<x<3\). Because x is restricted to integers, \(A=\{-2,-1,0,1,2\}\). The universal set contains all integers from -5 through 5, so removing A leaves \(A^c=\{-5,-4,-3,3,4,5\}\). The endpoints -3 and 3 are included in the complement because their squares equal 9, not a value less than 9.
Frequently asked questions
What is the correct answer to this question?
\(\{-5,-4,-3,3,4,5\}\)
Why is this the correct answer?
The condition \(x^2<9\) means \(-3<x<3\). Because x is restricted to integers, \(A=\{-2,-1,0,1,2\}\). The universal set contains all integers from -5 through 5, so removing A leaves \(A^c=\{-5,-4,-3,3,4,5\}\). The endpoints -3 and 3 are included in the complement because their squares equal 9, not a value less than 9.
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.
