Which statement is always true for all sets A, B, and C?
Answer and explanation
Correct answer: (A ∪ B) \ C = (A \ C) ∪ (B \ C)
An element belongs to (A ∪ B) \ C exactly when it is in A or B and is not in C. This is equivalent to saying that it is either in A \ C or in B \ C. Hence (A ∪ B) \ C = (A \ C) ∪ (B \ C), which is the distributive law of set difference over union. The other statements confuse union and intersection laws.
Frequently asked questions
What is the correct answer to this question?
(A ∪ B) \ C = (A \ C) ∪ (B \ C)
Why is this the correct answer?
An element belongs to (A ∪ B) \ C exactly when it is in A or B and is not in C. This is equivalent to saying that it is either in A \ C or in B \ C. Hence (A ∪ B) \ C = (A \ C) ∪ (B \ C), which is the distributive law of set difference over union. The other statements confuse union and intersection laws.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
