If A \ B = C and C ∩ B = ∅, what can be said about C ⊆ A?
Answer and explanation
Correct answer: It is always true
By definition, A \ B consists only of elements that belong to A and do not belong to B. Therefore every element of A \ B is automatically an element of A, which means A \ B ⊆ A. Since C = A \ B, it follows directly that C ⊆ A. The additional condition C ∩ B = ∅ is consistent with the definition but is not needed for this conclusion.
Frequently asked questions
What is the correct answer to this question?
It is always true
Why is this the correct answer?
By definition, A \ B consists only of elements that belong to A and do not belong to B. Therefore every element of A \ B is automatically an element of A, which means A \ B ⊆ A. Since C = A \ B, it follows directly that C ⊆ A. The additional condition C ∩ B = ∅ is consistent with the definition but is not needed for this conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
