To solve $X \cup (Y \cap Z)$ with the given sets, let's break down the problem step-by-step.

1. Identify $Y \cap Z$:

   • Set $Y = \{a, d, j, u, s, t\}$
   • Set $Z = \{s, u, b, j, e, c, t\}$
   • The intersection $Y \cap Z$ includes elements that are in both $Y$ and $Z$.
   • Common elements in $Y$ and $Z$ are $\{j, u, s, t\}$.

   So, $Y \cap Z = \{j, u, s, t\}$.

2. Form $X \cup (Y \cap Z)$:

   • Set $X = \{j, o, k, e, r\}$
   • We already found that $Y \cap Z = \{j, u, s, t\}$.
   • The union $X \cup (Y \cap Z)$ includes all unique elements from both $X$ and $Y \cap Z$.

   Combining the elements in $X$ and $Y \cap Z$ gives us: $X \cup (Y \cap Z) = \{j, o, k, e, r, u, s, t\}$

Therefore, the answer is: $X \cup (Y \cap Z) = \{j, o, k, e, r, u, s, t\}$

Would you like further clarification or additional details on any step?

Here are five related questions for further exploration:

1. What is the union of $Y$ and $Z$?
2. How would you find $X \cap (Y \cup Z)$?
3. If we add an element to $X$, how does it affect $X \cup (Y \cap Z)$?
4. What would $X \cap Y \cap Z$ look like?
5. Can you determine $(X \cup Y) \cap (X \cup Z)$?

Tip: When performing set operations, it’s often helpful to list elements in each set clearly to avoid missing any during union or intersection steps.