Which statement is generally not true?
Answer and explanation
Correct answer: A − B = B − A
Union and intersection are commutative operations, so changing the order of the sets does not change the result: A ∪ B = B ∪ A and A ∩ B = B ∩ A. Also, the union of any set with the empty set is the set itself. However, set difference depends on order. In general, A − B contains elements of A that are not in B, whereas B − A contains elements of B that are not in A. Therefore, A − B = B − A is generally false, although it may happen for special sets such as A = B.
Frequently asked questions
What is the correct answer to this question?
A − B = B − A
Why is this the correct answer?
Union and intersection are commutative operations, so changing the order of the sets does not change the result: A ∪ B = B ∪ A and A ∩ B = B ∩ A. Also, the union of any set with the empty set is the set itself. However, set difference depends on order. In general, A − B contains elements of A that are not in B, whereas B − A contains elements of B that are not in A. Therefore, A − B = B − A is generally false, although it may happen for special sets such as A = B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
