What Is Proof by Contradiction?

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Even the most experienced detectives encounter a puzzling case occasionally. You are sorting through facts and witness accounts which stated that two masked people fled the crime scene, immediately after screams for help were heard. After your investigation, you have narrowed your suspects down to five, Mr. Ashfield, Ms. Barlow, Mr. Caswell, Dr. Denton, and Mr. Everett. Two of these suspects are guilty and three are innocent. You are certain that:

• Ms. Barlow is involved with Mr. Ashfield and Mr. Everett, and would definitely be guilty if either (or both) of them are.
• Mr. Caswell vouched for Ms. Barlow, and so if Mr. Caswell is innocent, so is Ms. Barlow.
• If Dr. Denton is guilty and Mr. Ashfield is innocent, then Mr. Caswell is innocent as well.