If A, B, and C are sets and A ∩ B = A ∩ C, which statement is definitely true?
Answer and explanation
Correct answer: A ∩ (B △ C) = ∅
The equality A ∩ B = A ∩ C says that the elements common to A and B are exactly the same as the elements common to A and C. The symmetric difference B △ C contains elements belonging to exactly one of B or C. Since no such differing element can lie in A, their intersection with A is empty. However, B and C may still differ outside A, so B = C and the union statement are not necessarily true.
Frequently asked questions
What is the correct answer to this question?
A ∩ (B △ C) = ∅
Why is this the correct answer?
The equality A ∩ B = A ∩ C says that the elements common to A and B are exactly the same as the elements common to A and C. The symmetric difference B △ C contains elements belonging to exactly one of B or C. Since no such differing element can lie in A, their intersection with A is empty. However, B and C may still differ outside A, so B = C and the union statement are not necessarily true.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
