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reb659

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## Homework Statement

A function G:P--->R where R is the set of real numbers is additive provided

G(X1 U X2)=G(X1)+G(X2) if X1, X2 are disjoint.

Let S be a set, Let P be the power set of S. Suppose G is an additive function mapping P to R. Prove that if X1 and X2 are ARBITRARY(not necessarily disjoint subsets of W), then

G(X1 U X2)=G(X1)+G(X2)-G(X1 I X2)

## Homework Equations

## The Attempt at a Solution

The only way I know how to do this is using an element chasing proof. But if I let an element c be in the right hand side I can't go anywhere because the sets are not necessarily disjoint.

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