6. The set $X \backslash Y=\{a \mid a \in X, a \notin Y\}$ is called the difference set of set $X$ and set $Y$. Define the symmetric difference of sets $A$ and $B$ as $A \Delta B=(A \backslash B) \cup(B \backslash A)$.
If two non-empty finite sets $S$ and $T$ satisfy $|S \Delta T|=1$, then the minimum value of $k=|S|+|T|$ is $\qquad$.
6. 3 .

If $|S \Delta T|=1$, without loss of generality, assume
$$
\left\{\begin{array}{l}
|S \backslash T|=1, \\
|T \backslash S|=0,
\end{array}\right.
$$

i.e., $T$ is a proper subset of $S$, thus,
$$
|S|>|T| \geqslant 1 \text {. }
$$

Therefore, $k \geqslant|T|+1+|T| \geqslant 3$.
Construct sets $S=\{1,2\}, T=\{2\}$.
Clearly, the condition $|S \Delta T|=1$ is satisfied, and
$$
k=|S|+|T|=3 \text {. }
$$

Thus, $k_{\min }=3$.