1. (a) If Smith once beat the fireman at billiards, then Smith is not the fireman. Smith once beat the
fireman at billiards. If the brakeman is Jones, then Jones is not the fireman. The brakeman is
Jones. If Smith is not the fireman and Jones is not the fireman, then Robinson is the fireman. If
the brakeman is Jones and Robinson is the fireman, then Smith is the engineer. Therefore, Smith
is the engineer. (0— Smith once beat the fireman at billiards; M— Smith is the fireman; B— the
brakeman is Jones; N— Jones is the fireman; F— Robinson is the fireman; G– Smith is the
engineer.)