If A ∩ B = B, which statement about A \ B is not definitely true?
Answer and explanation
Correct answer: A \ B = ∅
The condition A ∩ B = B means that every element of B belongs to A, so B ⊆ A. However, A may contain additional elements outside B, or A may equal B. Therefore, A \ B may be non-empty or empty, and its emptiness is not guaranteed. The other three statements are identities or direct consequences of set difference, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
A \ B = ∅
Why is this the correct answer?
The condition A ∩ B = B means that every element of B belongs to A, so B ⊆ A. However, A may contain additional elements outside B, or A may equal B. Therefore, A \ B may be non-empty or empty, and its emptiness is not guaranteed. The other three statements are identities or direct consequences of set difference, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
