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Is the following statement true? "If f (Y − X) = f (Y ) − f...

Is the following statement true?

"If f (Y − X) = f (Y ) − f (X) for all sets X and Y with X ⊆ Y ⊆ A, then f : A → B is injective."

Please provide a proof if it is true, and a counterexample if it is false.

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