In what context is the statement A \ B = A ∩ B′ correct?
Answer and explanation
Correct answer: When B′ denotes the complement of B relative to the universal set U
By definition, A \ B consists of elements that are in A but not in B. Relative to a universal set U, the complement B′ contains precisely the elements of U that are not in B. Intersecting A with B′ therefore retains elements in A that are outside B, so A \ B = A ∩ B′. The universal set must be specified for the complement.
Frequently asked questions
What is the correct answer to this question?
When B′ denotes the complement of B relative to the universal set U
Why is this the correct answer?
By definition, A \ B consists of elements that are in A but not in B. Relative to a universal set U, the complement B′ contains precisely the elements of U that are not in B. Intersecting A with B′ therefore retains elements in A that are outside B, so A \ B = A ∩ B′. The universal set must be specified for the complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
