If A, B, and C are sets such that A − B = A − C and A ∩ B = A ∩ C, which statement is correct with respect to A?
Answer and explanation
Correct answer: Inside A, B and C have identical membership
For every element belonging to A, the first equality says that membership in B and membership in C as excluded elements are identical. The second equality confirms that the elements lying in both A and B are exactly those lying in both A and C. Therefore, B and C behave identically when restricted to A. They may still differ outside A, so B = C is not necessary.
Frequently asked questions
What is the correct answer to this question?
Inside A, B and C have identical membership
Why is this the correct answer?
For every element belonging to A, the first equality says that membership in B and membership in C as excluded elements are identical. The second equality confirms that the elements lying in both A and B are exactly those lying in both A and C. Therefore, B and C behave identically when restricted to A. They may still differ outside A, so B = C is not necessary.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
