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A delusion is a belief that is false but believed to be true. An example would be someone who thinks someone is trying to poison them and won't take needed medication due to the fear of being poisoned.
Dementia is a cognitive decline. Dementia is marked by memory problems most often. There are also deficits in reasoning and perceptions. However, when we think of dementia, memory is thes symptom that appears most often and is the most problematic.