Which of the following set identities is always true?
Answer and explanation
Correct answer: A ∪ B = B ∪ A
Union is commutative: A ∪ B = B ∪ A for every pair of sets because an element belongs to the union when it belongs to A or B, and changing the order does not change that condition. The other statements are not always true. In general A − B differs from B − A, A ∩ ∅ = ∅, and A ∪ A = A. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
A ∪ B = B ∪ A
Why is this the correct answer?
Union is commutative: A ∪ B = B ∪ A for every pair of sets because an element belongs to the union when it belongs to A or B, and changing the order does not change that condition. The other statements are not always true. In general A − B differs from B − A, A ∩ ∅ = ∅, and A ∪ A = A. Hence 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).
