deductive reasoning, law homework help

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After reading chapter 2 discuss induction versus deductive reasoning and how you would apply the concepts of each to the following unsolved crime scene:
Police Investigation
A man was found murdered and his wife severely beaten early on a Sunday morning in April 2001. The trailer park they lived in is a community of young adults just struggling to get by in life. The couple were newlyweds, Caucasian, in their early twenties and were expecting their first child.  The murder scene looked like a massacre.  The police found the female victim barely conscious leaning against the wall by the front door where she had struggled to get help but was weak from loss of blood. She had suffered blunt force trauma over her entire body. Her right little finger had been severed from her hand and was later found in a pool of blood.  She had also been raped while her husband lay dying in the bed next to her also suffering from blunt force trauma to his torso and head.
The trailer had been ransacked and various items were stolen to include video games, trading cards, and a gaming system. They had no money or items of any significant value. Tool marks could be found on the walls, interior of the front door, on the wooden floor of the bedroom where the attack occurred, and on the blades of the ceiling fan still spinning in the bedroom.  Blood could be found everywhere in the form of medium velocity spatter, drippings, pooling, trails, and cast-off.  Bloody shoe prints lead out the door and disappear in the dirt outside the back of the trailer. 
During the police investigation, a tire iron was found under a trailer near the back of the trailer park.  During the course of conducting a neighborhood canvas, detectives learned from residents that a large black male estimated to be in his thirties was seen wandering around the trailer park just prior to the time of murders. None of the residents recognized him as living in the trailer park or as a guest of anyone who lived in the trailer park. Detectives also learned that around the time of the murders, three teenage males were observed peeking in one of the trailer’s windows.

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