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$\renewcommand{\d}{\displaystyle}\newcommand{\N}{\mathbb N}\newcommand{\st}{:}\renewcommand{\bar}{\overline}\newcommand{\card}[1]{\left| #1 \right|}\renewcommand{\v}{\vtx{above}{}}\newcommand{\lt}{<}$

Let $A = \{n \in \N \st 20 \le n \lt 50\}$ and $B = \{n \in \N \st 10 \lt n \le 30\}\text{.}$ Suppose $C$ is a set such that $C \subseteq A$ and $C \subseteq B\text{.}$ What is the largest possible cardinality of $C\text{?}$

$\card{C} \le$