$A$ and $B$ are sets of real numbers defined as follows. \[ \begin{array}{l} A=\{x \mid x<3\} \\ B=\{x \mid x \geq 8\} \end{array} \] Write $A \cup B$ and $A \cap B$ using interval notation. If the set is empty, write $\varnothing$. \[ \begin{array}{l} A \cup B=\square \\ A \cap B=\square \\ (\square, \square) \quad[\square, \square] \quad(\square, \square] \\ {[\square, \square) \varnothing \quad \square \cup} \\ \infty \quad-\infty \\ \end{array} \]

Step 1 ：Define the sets $A$ and $B$ as $A=\{x \mid x<3\}$ and $B=\{x \mid x \geq 8\}$ respectively.

Step 2 ：The union of two sets, denoted $A \cup B$, is the set of elements that are in $A$, or in $B$, or in both. In this case, the union of $A$ and $B$ would be the set of all real numbers less than 3 or greater than or equal to 8.

Step 3 ：The intersection of two sets, denoted $A \cap B$, is the set of elements that are in both $A$ and $B$. In this case, since there are no real numbers that are both less than 3 and greater than or equal to 8, the intersection of $A$ and $B$ would be the empty set, denoted $\varnothing$.

Step 4 ：In interval notation, the set of all real numbers less than 3 is represented as $(-\infty, 3)$, and the set of all real numbers greater than or equal to 8 is represented as $[8, \infty)$. The union of these two sets would be represented as $(-\infty, 3) \cup [8, \infty)$, and the intersection would be represented as $\varnothing$.

Step 5 ：\(\boxed{A \cup B=(-\infty, 3) \cup [8, \infty)}\)

Step 6 ：\(\boxed{A \cap B=\varnothing}\)