If (A ∪ B) \ (A ∩ B) = ∅, what is true about A and B?
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Answer and explanation
Correct answer: A = B
The set (A ∪ B) \ (A ∩ B) consists of elements that belong to exactly one of A or B; it is the symmetric difference. If this set is empty, there are no elements occurring in only one set. Thus every element of A is in B and every element of B is in A, so A = B. The sets need not be empty.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The set (A ∪ B) \ (A ∩ B) consists of elements that belong to exactly one of A or B; it is the symmetric difference. If this set is empty, there are no elements occurring in only one set. Thus every element of A is in B and every element of B is in A, so A = B. The sets need not be empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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