$A$ and $B$ are sets of real numbers defined as follows.
\[
\begin{array}{l}
A=\{y \mid y \leq 1\} \\
B=\{y \mid y> 9\}
\end{array}
\]
Write $A \cup B$ and $A \cap B$ using interval notation. If the set is empty, write $\varnothing$.

Step 1 ：Let's first understand the definition of the sets $A$ and $B$. Set $A$ includes all real numbers $y$ that are less than or equal to 1. Set $B$ includes all real numbers $y$ that are greater than 9.

Step 2 ：The union of two sets, denoted as $A \cup B$, is a set that includes all the elements that are in $A$, or in $B$, or in both. In this case, $A \cup B$ includes all real numbers that are less than or equal to 1 or greater than 9. We can write this in interval notation as $(-\infty, 1] \cup (9, \infty)$.

Step 3 ：The intersection of two sets, denoted as $A \cap B$, is a set that includes all the elements that are in both $A$ and $B$. In this case, there are no real numbers that are both less than or equal to 1 and greater than 9. Therefore, $A \cap B$ is an empty set, which we write as $\varnothing$.

Step 4 ：Thus, the union of sets $A$ and $B$ is $\boxed{(-\infty, 1] \cup (9, \infty)}$ and the intersection of sets $A$ and $B$ is $\boxed{\varnothing}$.