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Trade Convention #1 - Logic Puzzles

Workers with the surnames Teacher, Baker, Carpenter, and Plumber are currently attending an annual convention.
No-one is currently, nor has ever been, in the same occupation as their name, and no-one has had the same occupation twice.
Charlie has never been a carpenter, and Mr Teacher is now a plumber.
Davie used to be a teacher, but Mr Billie Baker never has.
Mr Plumber is not called Eddie, and Mr Carpenter wasn't previously a teacher.
The previous occupations were all different, and the current occupations are all different.
Can you determine the full names of each of the attendees, along with their current and previous occupation?

Puzzle Copyright © Kevin Stone

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