If U = {p, q, r, s, t, u, v} and A = {p, r, t, v}, what is Aᶜ, the complement of A with respect to U?
Answer and explanation
Correct answer: {q, s, u}
The governing concept is the complement of a set relative to a stated universal set. Aᶜ contains every element of U that is not in A. From U = {p, q, r, s, t, u, v}, remove p, r, t, and v, because those four elements belong to A. The elements left are q, s, and u, so Aᶜ = {q, s, u}. Option A is A itself, while C is U and D is not justified; therefore B is correct.
Frequently asked questions
What is the correct answer to this question?
{q, s, u}
Why is this the correct answer?
The governing concept is the complement of a set relative to a stated universal set. Aᶜ contains every element of U that is not in A. From U = {p, q, r, s, t, u, v}, remove p, r, t, and v, because those four elements belong to A. The elements left are q, s, and u, so Aᶜ = {q, s, u}. Option A is A itself, while C is U and D is not justified; therefore B 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.
