up:: The image of the complement contains the complement of the images
Note that, by the definition of an Injective Function, we have that1
thus proving the reciprocal .
Footnotes
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That is due to . ↩
up:: The image of the complement contains the complement of the images
Note that, by the definition of an Injective Function, we have that1
∃x∈X∖B∣f(x)=y⟺(∃x∈X∣f(x)=y)∧(∄x∈B∣f(x)=y)thus proving the reciprocal f(X)∖f(B)⊆f(X∖B).
That is due to ∀y∈Y,∃!x∈X∣f(x)=y. ↩