Final answer:
The statement is false; serous membranes, not mucous membranes, line body cavities that do not have openings to the exterior of the body.
Step-by-step explanation:
Membranes that line body cavities that lack openings to the exterior of the body are actually called serous membranes, not mucous membranes. This statement is false. The mucous membranes, or mucosae, are indeed epithelial membranes, but they line body cavities and hollow passageways that open to the external environment, such as the digestive, respiratory, excretory, and reproductive tracts.
In contrast, serous membranes are mesodermally derived epithelial membranes that line the coelomic cavities, which do not open to the outside, and cover the organs within these cavities. The main serous membranes include the peritoneum in the abdominal cavity, the pleurae surrounding the lungs, and the pericardium around the heart.