If the universal set U has 35 elements and set A has 12 elements, how many elements does the complement A′ contain?
Answer and explanation
Correct answer: 23
For a finite set A contained in U, the elements of A and A′ together make up U and do not overlap. Therefore, n(U) = n(A) + n(A′), so n(A′) = n(U) − n(A). Substituting the given values gives n(A′) = 35 − 12 = 23. Thus, 23 elements belong to the complement. Option A is the size of A, option C is the size of U, and option D incorrectly adds the two quantities.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
For a finite set A contained in U, the elements of A and A′ together make up U and do not overlap. Therefore, n(U) = n(A) + n(A′), so n(A′) = n(U) − n(A). Substituting the given values gives n(A′) = 35 − 12 = 23. Thus, 23 elements belong to the complement. Option A is the size of A, option C is 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.
