$D$ and $E$ are sets of real numbers defined as follows. \[ \begin{array}{l} D=\{x \mid x>4\} \\ E=\{x \mid x \leq 8\} \end{array} \] Write $D \cap E$ and $D \cup E$ using interval notation. If the set is empty, write $\varnothing$.

Step 1 ：Define the sets $D$ and $E$ as follows: $D = \{x \mid x > 4\}$ and $E = \{x \mid x \leq 8\}$.

Step 2 ：Write these sets in interval notation. $D$ is $(4, \infty)$ and $E$ is $(-\infty, 8]$.

Step 3 ：Find the intersection of $D$ and $E$, denoted as $D \cap E$. This is the set of all numbers that are both greater than 4 and less than or equal to 8. In interval notation, this is $(4, 8]$.

Step 4 ：Find the union of $D$ and $E$, denoted as $D \cup E$. This is the set of all numbers that are either greater than 4 or less than or equal to 8. In interval notation, this is $(-\infty, \infty)$.

Step 5 ：\(\boxed{D \cap E = (4, 8]}\) and \(\boxed{D \cup E = (-\infty, \infty)}\)