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Wikipedia Description

In mathematics, the symmetric difference of two sets is the set of elements which are in either of the sets and not in their intersection. The symmetric difference of the sets A and B is commonly denoted byororFor example, the symmetric difference of the sets and is .The power set of any set becomes an abelian group under the operation of symmetric difference, with the empty set as the neutral element of the group and every element in this group being its own inverse. The power set of any set becomes a Boolean ring with symmetric difference as the addition of the ring and intersection as the multiplication of the ring.The symmetric difference is equivalent to the union of both relative complements, that is:The symmetric difference can also be expressed using the XOR operation on the predicates describing the two sets in set-builder notation:The same fact can be stated as the indicator function (which we denote here by ) of the symmetric difference being the XOR (or addition mod 2) of the indicator functions of its two arguments: or using the Iverson bracket notation .

backtracking, combination, puzzle