True or False: The parasympathetic system has no influence on peripheral vasculature.

The statement that the parasympathetic system has no influence on peripheral vasculature is indeed true because the primary role of the parasympathetic nervous system is to facilitate rest-and-digest functions, which includes the modulation of heart rate and glandular activity rather than direct control of peripheral blood vessels.

The parasympathetic system tends to induce vasodilation primarily through its influence on organs associated with its functions, such as the cardiac system, but it does not have a significant direct effect on peripheral vascular tone. Instead, it is the sympathetic nervous system that primarily modulates peripheral vasculature, controlling vasoconstriction and vasodilation through adrenergic receptors.

In summary, it is accurate to state that the influence of the parasympathetic nervous system on peripheral vasculature is minimal, as it does not play a major role in regulating blood vessel diameter outside of its primary actions on heart rate and gastrointestinal function.