MathNet 2020 — Math Olympiad Vault — Part 05 Question 102

Suppose $A=\{1,2, \ldots, 20\}$. Call $B$ a visionary set of $A$ if $B \subseteq A$, $B$ contains at least one even integer, and $|B| \in B$, where $|B|$ is the cardinality of set $B$. How many visionary sets does $A$ have?