If A = {1, 2, 3}, what is A ∪ ∅?
Answer and explanation
Correct answer: {1, 2, 3}
The union of two sets contains every element that belongs to at least one of them. The empty set ∅ contains no elements, so it contributes nothing when forming a union. Consequently, A ∪ ∅ = A. Since A = {1, 2, 3}, the result is {1, 2, 3}. Option A would be the result of confusing union with intersection in this situation, while options C and D introduce or omit elements without justification. This property is called the identity property of union.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3}
Why is this the correct answer?
The union of two sets contains every element that belongs to at least one of them. The empty set ∅ contains no elements, so it contributes nothing when forming a union. Consequently, A ∪ ∅ = A. Since A = {1, 2, 3}, the result is {1, 2, 3}. Option A would be the result of confusing union with intersection in this situation, while options C and D introduce or omit elements without justification. This property is called the identity property of union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
