Final answer:
It is false that veins do not contain elastic fibers. Both arteries and veins have elastic fibers within their walls, but arteries have a higher quantity to deal with greater blood pressure, whereas veins have valves and rely more on muscle contractions for blood flow.
Step-by-step explanation:
The statement 'arteries have elastic fibers, and veins do NOT' is false. Both arteries and veins possess elastic fibers within their walls. These fibers are essential for allowing arteries to expand and recoil as blood is pumped through them by the heart, necessary to withstand the higher pressures within arterial circulation. Meanwhile, veins also contain elastic fibers, although to a lesser extent than arteries, playing less of a role in maintaining vascular tension as the pressure within veins is lower.
Unlike arteries, veins have valves to prevent backflow of blood, particularly in areas where blood needs to be returned to the heart against the force of gravity, such as the lower limbs. While veins rely more on the contraction of skeletal muscle to assist blood flow back to the heart, both types of vessels have connective tissue comprising collagen and elastic fibers that support their structure.