If A ∩ B = A ∩ C and A \ B = A \ C, which conclusion must be true?
Answer and explanation
Correct answer: A ∩ (B Δ C) = ∅
The first equality says that within A, the elements belonging to B are exactly the same as those belonging to C. The second equality says that the elements of A outside B are exactly the same as the elements of A outside C. Hence no element of A can belong to exactly one of B and C. The symmetric difference B Δ C consists precisely of elements belonging to one set but not the other. Therefore A ∩ (B Δ C) = ∅, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
A ∩ (B Δ C) = ∅
Why is this the correct answer?
The first equality says that within A, the elements belonging to B are exactly the same as those belonging to C. The second equality says that the elements of A outside B are exactly the same as the elements of A outside C. Hence no element of A can belong to exactly one of B and C. The symmetric difference B Δ C consists precisely of elements belonging to one set but not the other. Therefore A ∩ (B Δ C) = ∅, so 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).
