If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{x:x\in U,\ x\ge 7\}\), what is \(A'\)?
Answer and explanation
Correct answer: \(\{1,2,3,4,5,6\}\)
The condition \(x\ge 7\) includes 7 and every larger element of the universal set. Thus, \(A=\{7,8,9,10\}\). The complement contains the elements of \(U\) that are not in \(A\), namely \(\{1,2,3,4,5,6\}\). Since the inequality includes equality, 7 belongs to \(A\), not to \(A'\). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3,4,5,6\}\)
Why is this the correct answer?
The condition \(x\ge 7\) includes 7 and every larger element of the universal set. Thus, \(A=\{7,8,9,10\}\). The complement contains the elements of \(U\) that are not in \(A\), namely \(\{1,2,3,4,5,6\}\). Since the inequality includes equality, 7 belongs to \(A\), not to \(A'\). Therefore, option A is correct.
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.
