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.
-Which of the following other propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
A) S ⊃ Y
B) ∼C ⊃ ∼S
C) S ⊃ ∼S
D) Options A, B, and C
E) Options A and B, but not option C

Question

Quizplus · Accepted Answer

The premises can be translated into propositional logic as follows: 1) S → C (If Sheldon writes a paper, using the copier is necessary for Yessenia to read it), 2) ∼Y → ∼S (Yessenia doesn't read it only if Sheldon doesn't write it, which is the contrapositive of Y → S). From these, we can derive that ∼C → ∼S (if the copier is not used, then Sheldon didn't write a paper) by contraposition of the first premise. However, S → ∼S (Sheldon writes a paper implies Sheldon does not write a paper) is a contradiction and cannot be derived from the given premises. Therefore, options A and B are derivable, but option C is not.

If Sheldon Writes a Paper, Then Using the Copier Is