If A \ (B ∩ C) is simplified, which option is correct?
Answer and explanation
Correct answer: (A \ B) ∪ (A \ C)
An element is in A \ (B ∩ C) if it belongs to A and does not belong to both B and C at the same time. Therefore, at least one of the conditions ‘not in B’ or ‘not in C’ must hold. The element is consequently in A \ B or in A \ C, giving A \ (B ∩ C) = (A \ B) ∪ (A \ C). The union is essential because either condition is sufficient.
Frequently asked questions
What is the correct answer to this question?
(A \ B) ∪ (A \ C)
Why is this the correct answer?
An element is in A \ (B ∩ C) if it belongs to A and does not belong to both B and C at the same time. Therefore, at least one of the conditions ‘not in B’ or ‘not in C’ must hold. The element is consequently in A \ B or in A \ C, giving A \ (B ∩ C) = (A \ B) ∪ (A \ C). The union is essential because either condition is sufficient.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
