$D$ and $E$ are sets of real numbers defined as follows. \[ \begin{array}{l} D=\{z \mid z<1\} \\ E=\{z \mid z \geq 7\} \end{array} \] Write $D \cup E$ and $D \cap E$ using interval notation. If the set is empty, write $\varnothing$. \[ D \cup E= \] \[ D \cap E= \]

Step 1 ：Define the sets $D$ and $E$ as $D=\{z \mid z<1\}$ and $E=\{z \mid z \geq 7\}$ respectively.

Step 2 ：The union of two sets, denoted by $D \cup E$, is the set of elements which are in $D$, in $E$, or in both. In this case, $D$ is the set of all real numbers less than 1 and $E$ is the set of all real numbers greater than or equal to 7. So, the union of these two sets would be the set of all real numbers less than 1 or greater than or equal to 7.

Step 3 ：The intersection of two sets, denoted by $D \cap E$, is the set of elements which are in both $D$ and $E$. In this case, since there are no real numbers that are both less than 1 and greater than or equal to 7, the intersection of these two sets would be an empty set.

Step 4 ：\(\boxed{D \cup E= (-\infty, 1) \cup [7, \infty)}\)

Step 5 ：\(\boxed{D \cap E= \varnothing}\)