If Sheldon writes a paper, then using the copier is a necessary condition for Yessenia reading it. Yessenia doesn't read it only if Sheldon doesn't write it. So, if Sheldon writes a paper, then he uses the copier.
-Consider assuming 'S' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
A) Y ⊃ C
B) S ⊃ Y
C) Y ⊃ S
D) Options A, B, and C
E) Options A and B, but not option C

Question

Quizplus · Accepted Answer

Assuming 'S' for conditional proof, we can use modus ponens to obtain 'Y ⊃ S' from the given premises ('If Sheldon writes a paper, then using the copier is a necessary condition for Yessenia reading it' and 'Yessenia doesn't read it only if Sheldon doesn't write it').

Then, using another application of modus ponens, we can obtain 'Y ⊃ C' from 'S ⊃ Y' (which is the contrapositive of the first given premise).

Therefore, the immediate (one-step) consequences in PL of the given premises with the assumption 'S' for conditional proof are 'Y ⊃ S' and 'Y ⊃ C', which correspond to options B and A, respectively. Option C is not an immediate consequence, but can be obtained by using modus ponens with 'Y ⊃ S' and the assumption 'S'.

If Sheldon Writes a Paper, Then Using the Copier Is