If A \ B = C \ B and A ∩ B = C ∩ B, what conclusion follows?
Answer and explanation
Correct answer: A = C
Every set can be partitioned into two disjoint parts relative to B: the elements outside B, represented by A \ B, and the elements inside B, represented by A ∩ B. The corresponding two parts of A and C are given to be equal. Therefore, A = (A \ B) ∪ (A ∩ B) and C = (C \ B) ∪ (C ∩ B) are unions of the same parts, so A = C. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = C
Why is this the correct answer?
Every set can be partitioned into two disjoint parts relative to B: the elements outside B, represented by A \ B, and the elements inside B, represented by A ∩ B. The corresponding two parts of A and C are given to be equal. Therefore, A = (A \ B) ∪ (A ∩ B) and C = (C \ B) ∪ (C ∩ B) are unions of the same parts, so A = C. Thus 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).
