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## Homework Statement

Find the useful denial of a injective function and a surjective function.

## Homework Equations

## The Attempt at a Solution

I know a one to one function is (∀x

_{1},x

_{2}∈ X)(x

_{1}≠x

_{2}⇒ f(x

_{1}) ≠ f(x

_{2})). So would the useful denial be (∃x

_{1},x

_{2}∈ X)(x

_{1}≠ x

_{2}∧ f(x

_{1}) = f(x

_{2}))?

I know a onto function is (∀y ∈ Y)(∃x ∈ X)(y=f(x)). So would the useful denial be (∃y ∈ Y)(∀x ∈ X)(y≠f(x))?

Thank you.