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To solve this problem, we need to find \( A' \), which is the complement of set \( A \) within the universal set \( U \). The complement of \( A \) consists of all elements in \( U \) that are *not* in \( A \).

Given:
- \( A = \{ y, o, g, u, r, t \} \)
- \( U = \{ a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z \} \)

### Step 1: List the elements in \( A \)
\( A \) contains: \( y, o, g, u, r, t \).

### Step 2: Identify elements in \( U \) but not in \( A \)
We go through each element in \( U \) and exclude those found in \( A \):

So, the elements in \( U \) but not in \( A \) are:
\[
A' = \{ a, b, c, d, e, f, h, i, j, k, l, m, n, p, q, s, v, w, x, z \}
\]

### Final Answer
The complement \( A' \) is:
\[
A' = \{ a, b, c, d, e, f, h, i, j, k, l, m, n, p, q, s, v, w, x, z \}
\]

Would you like a breakdown of any specific steps?

Here are some additional questions you might find helpful:
1. What is a universal set and how does it affect finding complements?
2. How can we represent sets and their complements using Venn diagrams?
3. How would we handle finding the complement if \( U \) were infinite (like all integers)?
4. What is the difference between a union and a complement?
5. How would the answer change if another element were added to set \( A \)?

**Tip**: When working with set complements, always double-check that you've excluded only the elements in the subset from the universal set.

If A = {y, o, g, u, r, t} 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 complement of a set within a universal set. This problem involves identifying elements in the universal set that are not in the subset A. Suitable for students in Grades 6-8.

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