I'm studying from a book and inside it I have this question:
Let $f:A\to B$ be a total function, which of the following states the $f$ is not injective:
A) For every $x,y \in A$ if $x=y$ then: $f(x) = f(y)$
B) There exist $f(x),f(y) \in B$ such that: $f(x) = f(y)$ and $x \ne y$
C) There exist $x,y \in A$ such that $f(x)=f(y)$ and $x \ne y$
First seeing this I almost instantly said that the correct answer is C, but in the book it says that the correct answer is B.
I kinda don't understand why B is true and C not, can anyone please tell me?