In a survey, it is given that \(n(U)=40\) and \(n(A^c)=15\). What is \(n(A)\)?
Answer and explanation
Correct answer: 25
For a set A and its complement A^c within the universal set U, every element of U belongs to exactly one of these two disjoint sets. Therefore, n(A)+n(A^c)=n(U). Substituting the given values gives n(A)+15=40, so n(A)=40−15=25. Hence option A is correct. Option C gives the complement’s size, option B exceeds the size of U, and option D ignores the given complement.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
For a set A and its complement A^c within the universal set U, every element of U belongs to exactly one of these two disjoint sets. Therefore, n(A)+n(A^c)=n(U). Substituting the given values gives n(A)+15=40, so n(A)=40−15=25. Hence option A is correct. Option C gives the complement’s size, option B exceeds the size of U, and option D ignores the given 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.
