Answer
$$1$$
Work Step by Step
We're asked to simplify $3+1+2+3$ in $\mathbb{Z}_4$. Using the associative property repeatedly, we can group this into the following form:
$$(((3+1)+2)+3)$$
Now, knowing the addition table for $\mathbb{Z}_4$, we simplify:
$$((0+2)+3)=((2)+3)=1$$
