It happened at an apartment complex on Bennington Street near Homestead Road around 3 a.m. Thursday.
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Houston police said officers were called to the apartment for a fight between a man and a woman, but when they arrived, the man had been shot in the torso and stabbed in both of his arms.
The woman was detained for questioning, HPD said.
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The man was transported to the hospital and is expected to survive. The 4-year-old child was not hurt.
Investigators said the incident could have possibly been a case of self-defense. The Harris County District Attorney's Office will determine if any charges will be filed.