To solve the problem in the image, we are tasked with finding $A'$, which represents the complement of set $A$ with respect to the universal set $U$.

Definitions:

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

The complement $A'$:

The complement $A'$ consists of all elements in $U$ that are not in $A$. To find $A'$:

1. Subtract the elements of $A$ from $U$.
2. Elements in $A$: $\{t, u, x, e, d, o, s\}$
3. Remove these from $U$.

Step-by-step Calculation:

From $U$: $U = \{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z\}$ Remove $\{t, u, x, e, d, o, s\}$, leaving: $A' = \{a, b, c, f, g, h, i, j, k, l, m, n, p, q, r, v, w, y, z\}.$

Final Answer:

$A' = \{a, b, c, f, g, h, i, j, k, l, m, n, p, q, r, v, w, y, z\}.$

Would you like me to verify or explain further? Let me know!

Here are 5 relative questions to expand your understanding:

1. What is the difference between complement and union of sets?
2. How can a Venn diagram represent the complement of a set?
3. How do intersections and complements relate in set theory?
4. What happens if $A$ is the universal set $U$?
5. Can complements be applied to infinite sets, and if so, how?

Tip: To quickly verify complements, count elements in $A$, $U$, and $A'$ to ensure $|A| + |A'| = |U|$.