Which of the following statements about the complement of a set, with respect to a universal set, is always true?
Answer and explanation
Correct answer: The intersection of a set and its complement is the empty set.
The complement A^c consists precisely of the elements of the universal set U that are not in A. Therefore, no element can belong to both A and A^c, which gives A∩A^c=∅. At the same time, every element of U belongs to either A or A^c, so A∪A^c=U. Hence option A is the only universally true statement.
Frequently asked questions
What is the correct answer to this question?
The intersection of a set and its complement is the empty set.
Why is this the correct answer?
The complement A^c consists precisely of the elements of the universal set U that are not in A. Therefore, no element can belong to both A and A^c, which gives A∩A^c=∅. At the same time, every element of U belongs to either A or A^c, so A∪A^c=U. Hence option A is the only universally true statement.
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.
