JNU SSS 2012 Question 66: Sets, relations and functions

A relation $f$ from set $X$ to set $Z$ is a function if and only if for every element $x$ in $X$ there is a unique element $z$ in $Z$ such that $x$ and $z$ are associated through $f$. $X$ is called the domain of $f$ and $Z$ the codomain of $f$. The range of $f$ is the set of all elements in the codomain which are associated with at least one element in the domain. $f$ is a surjective function if and only if every element in the codomain has an association in the domain. $f$ is an injective function if and only if no two distinct elements in the domain are associated with the same element in the codomain. Consider the following statements : (i) There exists an element $x$ in the domain of $f$ such that no element in the codomain is associated with it. (ii) There exists an element $x$ in the domain of $f$ and two distinct elements $z$ and $w$ in the codomain of $f$ such that both $z$ and $w$ are associated with $x$.

Which of the following is true?