Math, asked by raziisamawal07, 1 month ago

Define and prove two identities of symmetric identities A ⊕ B

Answers

Answered by NoExist
2

Answer:

Symmetric Difference. Definition: The symmetric difference of set A and set B, denoted by A ⊕ B, is the set containing those elements in exactly one of A and B. Formally: A ⊕ B = (A − B) ∪ (B − A).

Step-by-step explanation:

Patrick's got it. Here's the same, in a somewhat different presentation.

The symmetric difference of two sets is the stuff that's in exactly one of the two sets. If the symmetric difference of A and B is A, then B can't have any elements that are in A (since those elements of A wouldn't be in the symmetric difference), and B can't have any elements that aren't in A (since those non-elements of A would be in the symmetric difference), so B can't have any elements. Thus if B is to be the identity, B must be empty; moreover, if B is empty, it works as an identity element for symmetric difference

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