Which of the following set identities is true for all sets A, B, and C?
Answer and explanation
Correct answer: A \ (B ∪ C) = (A \ B) ∩ (A \ C)
An element belongs to A \ (B ∪ C) precisely when it belongs to A and belongs to neither B nor C. The condition of being outside the union B ∪ C therefore means being outside both B and C. This is exactly the membership condition for (A \ B) ∩ (A \ C). Thus option A is De Morgan’s difference identity and is true for all sets.
Frequently asked questions
What is the correct answer to this question?
A \ (B ∪ C) = (A \ B) ∩ (A \ C)
Why is this the correct answer?
An element belongs to A \ (B ∪ C) precisely when it belongs to A and belongs to neither B nor C. The condition of being outside the union B ∪ C therefore means being outside both B and C. This is exactly the membership condition for (A \ B) ∩ (A \ C). Thus option A is De Morgan’s difference identity and is true for all sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
