Final answer:
Marfan's syndrome is strongly associated with mitral valve prolapse and aortic dissection, both of which affect the functioning of the heart valves and can be serious conditions.
Step-by-step explanation:
The two heart conditions strongly associated with Marfan's syndrome are a) Mitral valve prolapse and aortic dissection. Mitral valve prolapse occurs when the mitral valve doesn't close properly, causing blood to leak backwards into the upper chamber of the heart. Aortic dissection is a serious condition where the inner layer of the aorta tears, allowing blood to flow between the layers of the artery wall.