Question: II. (A) Symbolize the following arguments using the letters provi...
II. (A) Symbolize the following arguments using the letters provided, and (b) show that each
argument is valid by constructing proofs of their conclusions from their premises using the
rules of inference we have studied in this course. (12/50)
(a) Ir Smith once beat the fireman at billiards, then Smith is not the fireman Smith once beat the
fireman at billiards. If the brakemanis Jones, then Jones is not the fireman. The brakemanis Jones,
1 Smith is not the fireman and Jones is not the fireman, then Robinson is the fireman. If the
brakemanis Jones and Robinson is the fireman, then Smith is the engineer. Therefore, Smith is the
engineer (O-Smith once beat the fireman at billiards M-Smith is the fireman - the
brakemanis Jones: N-Jones is the fireman F-Robinson is the fireman, G-Smith is the
engineer)
(b) If Xavier takes Spanish, then Yolanda tutors him. Zeke pays Yolanda if she tutoes Xavier. Either
Waldo or Xavier takes Spanish Waldo does not take Spanish; also Yolanda doesn't tutor Xavier
So, Zeke pays Yolanda, but Waldo doesn't take Spanish. (X-Xavier takes Spanish: Y-Yolanda
tutors Xavier, Z-Zeke pay Yolanda: W- Waldo takes Spanish)
(c) I Anderson was nominated, then she went to Boston. If she went to Boston, then she campaigned
there. If she campaigned there she met Douglas Anderson did not meet Douglas. Either Anderson
was nominated or someone more eligible was selected. Therefore, someone more eligible was
sclected.( Anderson was nominated: Anderson went to Boston, Anderson
campaigned in Boston, Anderson met Douglas; E-Someone more eligible was selected.)
(d) If Santacruz is injured, then she will not play. And if Santacruz does not play, then Khumalo must
play, What's is more, ir Khumalo and Nakata both play, then Jones must be moved to the center. In
fact, Santacruz is injured and Nakata will play. Thus, Khumalo will play Jones will be moved into
the center. (1 Santacruz is injured: S-Santacruz will play, K-Khumalo must play: N Nakata
plays, Jones must be moved to the center)