Which statement proves that A and A^c together form a partition of U?
Answer and explanation
Correct answer: A∩A^c=∅ and A∪A^c=U
A partition of U requires two essential conditions: its parts must be pairwise disjoint, and their union must be the whole universal set. A and A^c are disjoint because no element can belong to both, so A∩A^c=∅. Together they contain every element of U, so A∪A^c=U. Therefore, option A proves that they form a partition.
Frequently asked questions
What is the correct answer to this question?
A∩A^c=∅ and A∪A^c=U
Why is this the correct answer?
A partition of U requires two essential conditions: its parts must be pairwise disjoint, and their union must be the whole universal set. A and A^c are disjoint because no element can belong to both, so A∩A^c=∅. Together they contain every element of U, so A∪A^c=U. Therefore, option A proves that they form a partition.
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.
