If n(U) = 40 and n(A) = 18, what is n(Aᶜ)?
Answer and explanation
Correct answer: 22
The governing cardinality rule for a finite universal set is n(Aᶜ) = n(U) − n(A), because U is partitioned into A and its complement. Substituting the given values gives n(Aᶜ) = 40 − 18 = 22. Thus 22 elements are outside A but still inside U, so option B is correct. Option A repeats n(A), option C repeats the size of U, and option D incorrectly adds the two quantities.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The governing cardinality rule for a finite universal set is n(Aᶜ) = n(U) − n(A), because U is partitioned into A and its complement. Substituting the given values gives n(Aᶜ) = 40 − 18 = 22. Thus 22 elements are outside A but still inside U, so option B is correct. Option A repeats n(A), option C repeats the size of U, and option D incorrectly adds the two quantities.
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.
