https://file.aiquickdraw.com/mathbot/file/1730769322048zrsgknqj.jpg

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.

If A = {m, i, c, r, o, w, a, v, e} and 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}, find |A'|.

Learn how to find the cardinality of the complement of a set A in a universal set U. This problem involves set theory concepts, including the set complement and calculating cardinality by subtracting the elements of A from U. Suitable for students in Grades 8-10.

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