If \(n(U)=36\) and \(n(A)=14\), what is \(n(A^c)\)?
Answer and explanation
Correct answer: 22
For a finite universal set, A and A^c together contain every element of U and have no common elements. Hence n(A)+n(A^c)=n(U), so n(A^c)=n(U)−n(A). Substituting the values gives n(A^c)=36−14=22. Thus option A is correct. Option C is the size of A, option D is the size of U, and option B is an incorrect sum rather than the required difference.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
For a finite universal set, A and A^c together contain every element of U and have no common elements. Hence n(A)+n(A^c)=n(U), so n(A^c)=n(U)−n(A). Substituting the values gives n(A^c)=36−14=22. Thus option A is correct. Option C is the size of A, option D is the size of U, and option B is an incorrect sum rather than the required difference.
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.
