The symmetric difference of set identity, also known as the symmetric difference or exclusive OR (XOR) of two sets, is a mathematical operation that compares two sets and returns a new set containing elements that are unique to each set.
The symmetric difference of set identity can be represented using the symbol "∆" or "⊕". For example, if A and B are two sets, their symmetric difference can be denoted as A ∆ B or A ⊕ B.
The symmetric difference of set identity differs from the union of sets in that the union combines all elements from both sets, while the symmetric difference only includes elements that are unique to each set.
The symmetric difference of set identity has various applications in computer science, such as in database operations, error detection and correction, and cryptography. It is also used in genetics to compare DNA sequences and identify genetic variations.
No, a set cannot have a symmetric difference with itself because the resulting set would be empty. This is because there are no elements unique to both sets when they are the same.