Solution
= Solution
\b[True.] The assumptions give
$$
t_B-t_A\geq|x_B-x_A|,
\qquad t_A-t_C\geq|x_A-x_C|.
$$
Adding and applying the triangle inequality proves
$$
t_B-t_C\geq|x_B-x_A|+|x_A-x_C|
\geq|x_B-x_C|,
$$
so $B$ is in the future lightcone of $C$.