Puzzles

This morning, the body of Vice-Principal Vindictive was found. He had choked to death on chalk dust, to which he was fatally allergic. Vindictive never used chalk, so this wasn't an accidental death: it was murder. The list of suspects has been narrowed to the four students who were meeting individually with Vindictive yesterday afternoon. The following facts have been determined; can you find the killer?

Every student flunking both English and American History is passing Algebra.
Every student flunking American History, but passing Algebra, is also passing English.
Every student flunking American History, but passing English, is also passing Shop.
Every student flunking Shop, but passing Chemistry, is also flunking American History.
Every student flunking Chemistry, but passing American History, is also flunking English.

Upon searching Vindictive's body, detectives found a torn scrap of paper clutched in his right hand. It turned out to be part of a report card: the killer was flunking Shop.

The following students were meeting with Vice-Principal Vindictive yesterday afternoon. Which one of them dusted the teacher?

Anita, who is flunking English and passing Chemistry
Brian, who is flunking Chemistry and passing American History
Chloe, who is flunking American History and passing Algebra
David, who is flunking Algebra and passing English

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