If $A$ and $B$ are two sets where the number of elements in set $A$ is $28$, the number of elements in set $B$ is $35$, and the number of elements common to both sets $A$ and $B$ is $12$, determine $n(A\cup B)$.

According to the principle of inclusion-exclusion for any two finite sets $A$ and $B$:
$$n(A\cup B)=n(A)+n(B)-n(A\cap B)$$

Given the values from the problem statement:

* $n(A)=28$
* $n(B)=35$
* $n(A\cap B)=12$ (elements common to both sets)

Substitute these values into the formula:

$$n(A\cup B)=28+35-12$$

$$n(A\cup B)=63-12$$

$$n(A\cup B)=51$$

Therefore, the value of $n(A\cup B)$ is $51$.