Final answer:
The mental illness most commonly associated with the neglect of basic personal hygiene and carelessness is schizophrenia, a disorder that affects a person's thinking, feelings, and behavior.
Step-by-step explanation:
The question pertains to mental illnesses, specifically focusing on the symptoms of neglect of basic personal hygiene and carelessness. When evaluating these symptoms, the mental illness that most commonly is associated with these signs is schizophrenia.
Schizophrenia is a complex mental disorder that affects how a person thinks, feels, and behaves. It can lead to a range of symptoms, including delusions, hallucinations, disorganized thinking, and significant impairment in social functioning, such as neglecting personal hygiene.
On the other hand, Attention Deficit Hyperactivity Disorder (ADHD) is characterized by difficulty maintaining attention and controlling impulses, but it's not typically associated with the neglect of personal hygiene. More severe symptoms like the neglect of personal hygiene are more often observed in disorders like schizophrenia.