The universal set $U$ is given as:

$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$

The given set is:

$A = \{x \ | \ x \in W \ \text{and} \ x < 8\}$

Here, $W$ represents the set of whole numbers, and whole numbers include all non-negative integers. Thus, we are looking for values of $x$ from $U$ that are less than 8. Therefore, the set $A$ will include:

$A = \{0, 1, 2, 3, 4, 5, 6, 7\}$

The complement of a set $A$, denoted $A^c$, is the set of elements in $U$ that are not in $A$. So the complement of $A$ is:

$A^c = U - A = \{8, 9, 10, 11, 12\}$

Thus, the complement of the set is:

$A^c = \{8, 9, 10, 11, 12\}$

Do you have any questions or need further clarification?

Here are some related questions for practice:

1. What is the complement of the set $\{2, 4, 6\}$ in $U = \{0, 1, 2, 3, 4, 5, 6, 7\}$?
2. If $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, what is $A^c \cap B$?
3. Find the union of sets $A = \{0, 2, 4\}$ and $B = \{1, 2, 3\}$.
4. What is the intersection of $A = \{1, 3, 5, 7\}$ and $B = \{2, 3, 6\}$?
5. If $U = \{a, b, c, d, e\}$, what is the complement of $A = \{b, d\}$?

Tip: The complement of a set always contains every element from the universal set that is not in the original set.