The length of a rod is measured by an experimenter. Initially, both...

The proper length of the rod is measured when both the rod and the observer are at rest relative to each other. Let this length be $L_0$.

According to the special theory of relativity, when there is a relative velocity $v$ between the rod and the observer parallel to the length of the rod, the measured length $L$ is given by the length contraction formula $L = L_0 \sqrt{1 - \dfrac{v^2}{c^2}}$.

In statement A, the rod moves with respect to the stationary observer, creating a relative velocity. Thus, the measured length decreases.

In statement B, the observer moves with respect to the stationary rod, which also creates a relative velocity. Thus, the measured length decreases as well.

Therefore, both statements A and B are true.