If \(A=\{1,2\}\), \(U_1=\{1,2,3\}\), and \(U_2=\{1,2,3,4\}\), why is the complement of A different in the two cases?
Answer and explanation
Correct answer: Because the universal set changes
The complement of A is always defined relative to a specified universal set: A^c=U−A. With U_1, the complement is {3}; with U_2, the complement is {3,4}. The set A itself remains unchanged in both situations, but the collection of available elements outside A changes because the universal set changes. Hence option A correctly identifies the reason.
Frequently asked questions
What is the correct answer to this question?
Because the universal set changes
Why is this the correct answer?
The complement of A is always defined relative to a specified universal set: A^c=U−A. With U_1, the complement is {3}; with U_2, the complement is {3,4}. The set A itself remains unchanged in both situations, but the collection of available elements outside A changes because the universal set changes. Hence option A correctly identifies the reason.
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.
