If A Δ B denotes the symmetric difference of A and B, what does (A Δ B)' represent?
Answer and explanation
Correct answer: Elements are in both sets or in neither set
The symmetric difference A Δ B consists of elements belonging to exactly one of A or B. In logical terms, these elements satisfy exclusive OR. Taking its complement selects all elements for which exclusive OR is false: an element is either in both A and B or in neither set. Thus (A Δ B)' = (A ∩ B) ∪ (A' ∩ B'), represented by option A.
Frequently asked questions
What is the correct answer to this question?
Elements are in both sets or in neither set
Why is this the correct answer?
The symmetric difference A Δ B consists of elements belonging to exactly one of A or B. In logical terms, these elements satisfy exclusive OR. Taking its complement selects all elements for which exclusive OR is false: an element is either in both A and B or in neither set. Thus (A Δ B)' = (A ∩ B) ∪ (A' ∩ B'), represented by option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
