Canonical Projection I hope are well. I have some doubts as I am new in algebra. 
Let $V/W$ the quotient vector space with the usual sum and product, in addition to the equivalence relation defined on $W$ which is a subspace of $V$.
How I can prove that the canonical projection that sends a vector $v$ of $V$ to its equivalence class in $V/W$ is not injective but it's surjective?

I recommend, investigate the universal property of quotient vector space.
