If |U| = 15 and |A'| = 6, what is |A|?
Answer and explanation
Correct answer: 9
A set A and its complement A' divide the universal set U into two disjoint parts. Therefore, |A| + |A'| = |U|. Substituting the given values gives |A| + 6 = 15, so |A| = 15 − 6 = 9. Hence option B is correct. The answer cannot be 6 because that is the size of A', and it cannot be 15 because A is only one part of U. The complement relation also guarantees that the two cardinalities add to the universal-set cardinality.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
A set A and its complement A' divide the universal set U into two disjoint parts. Therefore, |A| + |A'| = |U|. Substituting the given values gives |A| + 6 = 15, so |A| = 15 − 6 = 9. Hence option B is correct. The answer cannot be 6 because that is the size of A', and it cannot be 15 because A is only one part of U. The complement relation also guarantees that the two cardinalities add to the universal-set cardinality.
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.
