ALAAKARBOUJGO
Cevaplandı

. For an arbitrary set X, define an addition on the power set P(X) of X by A + B = A ∪ B − A ∩ B = (A − B) ∪ (B − A) for any two subsets A and B of X. Prove that P(A) is a group with respect to this operation of addition.​

Cevap :

POTIPORI75GO

Answer: Additive Group Conditions: Identity Element, Additive Inverse and Associativity

Verify

Identity element: A+e=e+A=A (is there an e set?) for the empty set (A-empty set) ∪ (Empty set-A) = A ∪ empty set = A yeah the empty is identity element for this operation

Additive Inverse A+(-A)=(-A+A)=empty set it is easy that every element under this operation is an inverse of itself.

Associativity is easy so it is omitted.

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