If A = {2, 4}, U₁ = {1, 2, 3, 4}, and U₂ = {1, 2, 3, 4, 5}, why can Aᶜ have two different values?
Answer and explanation
Correct answer: Because the universal set has changed
A complement is not determined by A alone; it is defined with respect to a specified universal set. Relative to U₁, Aᶜ = U₁ − A = {1, 3}. Relative to U₂, Aᶜ = U₂ − A = {1, 3, 5}. Thus the extra element 5 appears when the universal set changes. Set A itself remains unchanged, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Because the universal set has changed
Why is this the correct answer?
A complement is not determined by A alone; it is defined with respect to a specified universal set. Relative to U₁, Aᶜ = U₁ − A = {1, 3}. Relative to U₂, Aᶜ = U₂ − A = {1, 3, 5}. Thus the extra element 5 appears when the universal set changes. Set A itself remains unchanged, so 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.
