If \(U=\{p,q,r,s,t\}\) and \(A=\{p,s,t\}\), find \(A^c\).
Answer and explanation
Correct answer: \(\{q,r\}\)
The complement A^c contains exactly those elements of U that are absent from A. The universal set lists p, q, r, s, and t, while A contains p, s, and t. Removing these three elements from U leaves q and r. Therefore, A^c={q,r}, making option A correct. Option B repeats A, option C incorrectly includes p, and option D leaves out q.
Frequently asked questions
What is the correct answer to this question?
\(\{q,r\}\)
Why is this the correct answer?
The complement A^c contains exactly those elements of U that are absent from A. The universal set lists p, q, r, s, and t, while A contains p, s, and t. Removing these three elements from U leaves q and r. Therefore, A^c={q,r}, making option A correct. Option B repeats A, option C incorrectly includes p, and option D leaves out q.
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.
