If A \ (B ∪ C) is described using only the meaning of A, B, C, ∩, and set difference, which elements does it contain?
Answer and explanation
Correct answer: Elements in A but in neither B nor C
The union B ∪ C contains every element that belongs to B, to C, or to both. The difference A \ (B ∪ C) therefore removes from A every element found in either B or C. What remains consists of elements that are in A, not in B, and not in C. Equivalently, it can be written as A ∩ Bᶜ ∩ Cᶜ, so option A gives the precise meaning.
Frequently asked questions
What is the correct answer to this question?
Elements in A but in neither B nor C
Why is this the correct answer?
The union B ∪ C contains every element that belongs to B, to C, or to both. The difference A \ (B ∪ C) therefore removes from A every element found in either B or C. What remains consists of elements that are in A, not in B, and not in C. Equivalently, it can be written as A ∩ Bᶜ ∩ Cᶜ, so option A gives the precise meaning.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
