If A and B are disjoint sets, which of the following statements is correct?
Answer and explanation
Correct answer: A intersection B = the empty set
Two sets are called disjoint when they have no common element. The set containing elements common to both sets is their intersection, so the definition is written as A intersection B = the empty set. Disjoint sets need not themselves be empty; for example, {1, 2} and {3, 4} are disjoint. Therefore, A union B need not be empty, the sets need not be equal, and neither set must be a subset of the other. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
A intersection B = the empty set
Why is this the correct answer?
Two sets are called disjoint when they have no common element. The set containing elements common to both sets is their intersection, so the definition is written as A intersection B = the empty set. Disjoint sets need not themselves be empty; for example, {1, 2} and {3, 4} are disjoint. Therefore, A union B need not be empty, the sets need not be equal, and neither set must be a subset of the other. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
