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## Homework Statement

Is the minimum function defined by f(a,b)=min{a,b} surjective or injective?

## Homework Equations

a function is injective f(x)=f(y) always implies x=y.

a function is surjective if for every y in codomain, there exists an x in domain such that f(x)=y.

## The Attempt at a Solution

I am confused whether min is surjective function or not.

As for injective, it is not. e.g. f(2,3) and f(3,2) both give 2. This is sufficient to say it is not injective.

But it is surjective, which I am mostly sure, but how do I show it is surjective?