The problem provided is as follows:

Given:

• Set $A = \{ m, i, c, r, o, w, a, v, e \}$
• Universal set $U = \{ a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z \}$

You are asked to find $|A'|$, where $A'$ is the complement of set $A$ in the universal set $U$.

Solution

1. The complement $A'$ includes all elements in $U$ that are not in $A$.
2. First, list out elements in $U$ and remove elements that are also in $A$.

From $U$:

• Elements in $A$ are: $m, i, c, r, o, w, a, v, e$.

After removing these, the elements in $A'$ are: $b, d, f, g, h, j, k, l, n, p, q, s, t, u, x, y, z$.

3. Count the elements in $A'$:
   • There are 17 elements in $A'$.

Answer

$|A'| = 17$.

Would you like more details on the steps, or have any questions?

Related Questions

1. What is the difference between a set and its complement?
2. How would the answer change if we modified $A$ or $U$?
3. How can we apply the concept of set complements to solve real-world problems?
4. What would happen to $|A'|$ if we removed elements from $U$?
5. How does the size of $U$ affect the size of $A'$?

Tip

To find the complement of a set, carefully list all elements in the universal set, then exclude any element that also appears in the original set.