Awoman says the following illogical sentences: "the eagle takes flight at three o’clock and flies here from general electric. i get my check from the eagle; he goes from the mailbox to make a payment. he is a secret spy for my husband and makes a shotgun sound." based on what she says, this woman is most likely experiencing and is displaying a symptom.

The woman is experiencing schizophrenia and is displaying a positive symptom.

Explanation:

Schizophrenia is a mental disorder primarily characterized by hallucinations and delusions, as well as a disorganization in speech, abnormal motor behavior and negative symptoms.

Let's break down the first two:

Mental disorders tend to have 2 types of symptoms:

In this case, the woman has the delusion that an eagle is a secret spy for her husband and has the hallucination that it makes a shotgun sound. Her belief that the eagle delivers her check is perceived as her reality.

The woman is displaying positive symptoms of schizophrenia, understood as the hallucinations and delusions.

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