If the universal set U = {1, 2, 3, 4, 5, 6} and A = {1, 2, 3}, which set B satisfies B = Aᶜ?
Answer and explanation
Correct answer: {4, 5, 6}
Aᶜ is defined relative to the stated universal set U. It contains every element of U that is not an element of A. Starting with U = {1, 2, 3, 4, 5, 6} and removing A = {1, 2, 3} leaves {4, 5, 6}. Therefore, Aᶜ = {4, 5, 6}, so the set B satisfying B = Aᶜ is option A. The universal set must always be used when determining a complement.
Frequently asked questions
What is the correct answer to this question?
{4, 5, 6}
Why is this the correct answer?
Aᶜ is defined relative to the stated universal set U. It contains every element of U that is not an element of A. Starting with U = {1, 2, 3, 4, 5, 6} and removing A = {1, 2, 3} leaves {4, 5, 6}. Therefore, Aᶜ = {4, 5, 6}, so the set B satisfying B = Aᶜ is option A. The universal set must always be used when determining a complement.
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.
