To determine which of the arrow diagrams represents an onto function, we must recall that an onto function (or surjective function) is one where every element in the target set $Y$ has at least one element in the domain $X$ that maps to it. This means every element in $Y$ is covered by the mapping from $X$.

Let's analyze each diagram:

Diagram I

In Diagram I, the elements in set $X = \{1, 2, 3\}$ are mapped to elements in set $Y = \{a, b, c\}$. Checking the connections:

• $1 \rightarrow a$
• $2 \rightarrow b$
• $3 \rightarrow b$

In this mapping:

• $a$ has one pre-image (from 1),
• $b$ has two pre-images (from 2 and 3),
• $c$ has no pre-image.

Since $c$ in $Y$ is not mapped to by any element in $X$, Diagram I is not onto.

Diagram II

In Diagram II, $X = \{1, 2, 3, 4\}$ and $Y = \{a, b, c\}$. The mappings are as follows:

• $1 \rightarrow a$
• $2 \rightarrow b$
• $3 \rightarrow c$
• $4 \rightarrow c$

In this mapping:

• $a$ has one pre-image (from 1),
• $b$ has one pre-image (from 2),