Solution:

According to Cartesian sign convention, the focal length of a convex mirror is always positive as its principal focus is virtual and lies behind the mirror. Thus, (A) is false. While sign conventions involve directions, stating that distances measured in the direction of incident rays 'may be taken as negative' is generally incorrect or misleading; typically, these are taken as positive. Hence, (R) is also false. Thus, both (A) and (R) are false.