1. The problem is to understand the expression $x \cap (y \cup z)$, which involves set operations: intersection ($\cap$) and union ($\cup$). 2. The union of two sets $y$ and $z$ is the set of all elements that are in $y$, or in $z$, or in both. It is written as: $$y \cup z = \{a : a \in y \text{ or } a \in z\}$$ 3. The intersection of a set $x$ with another set is the set of all elements that are common to both sets. So, $$x \cap (y \cup z) = \{a : a \in x \text{ and } a \in (y \cup z)\}$$ 4. This means the elements in $x$ that are also in either $y$ or $z$. 5. There is no further simplification without knowing the specific elements of $x$, $y$, and $z$. The expression is already in its simplest set-theoretic form. Final answer: $x \cap (y \cup z)$ is the set of elements common to $x$ and the union of $y$ and $z$.