Analyze each proof.  Decide if the proof is correct, or if the proof has an error. Inelegant proofs are not necessarily incorrect. 1. (L ≡ N) ⊃ C 2. (L ≡ N) v (P ⊃ ~E) 3. ~E ⊃ C 4. ~C/ ~P 5. ~(L ≡ N)Modus Tollens 1, 4 6. P ⊃ ~EDisjunctive Syllogism 2, 5 7. ~~EModus Tollens 3, 4 8. ~PModus Tollens 6, 7

My computer has the Office 365 Apps (Word, Excel, Powerpoint, etc.) and I know how to access the Office 365 versions on the web.

What is the correct inference rule for C5? P1. If humans do not have free will, then humans are not morally responsible. P2. Humans are morally responsible. ∴ C1.  Humans do have free will. P3. If humans do have free will, then humans can generate events that are not the effect of a prior cause. ∴ C2.  Humans can generate events that are not the effect of a prior cause. P4. The gods can generate events that are not the effect of a prior cause. ∴ C3.  Humans can generate events that are not the effect of a prior cause, and the gods can generate events that are not the effect of a prior cause. P5. If Humans can generate events that are not the effect of a prior cause, and the gods can generate events that are not the effect of a prior cause, then humans are like the gods. P6. If humans are like gods, then humans can do anything within the realm of possibility. ∴ C4.  If humans can generate events that are not the effect of a prior cause and the gods can generate events that are not the effect of a prior cause, then humans can do anything within the realm of possibility. ∴ C5.Humans can do anything within the realm of possibility.

If the sun is a variable star, then the sun’s energy will drop drastically at some point in the future.  If the sun’s energy drops drastically at some point in the future, then the Earth will become a giant iceball.  Therefore, if the sun is a variable star, then the Earth will become a giant iceball. What type of argument is this?

No disobedient children are honor roll students. No honor roll students are delinquents. Therefore, some delinquents are disobedient children.      What is the mood of this argument?

Analyze each proof.  Decide if the proof is correct, or if the proof has an error. Inelegant proofs are not necessarily incorrect. 1. R ⊃ S 2. (Q ⊃ S) ⊃ ~P 3. ~P ⊃ [ (Q ⊃ R) ⊃ (L v ~S)] 4. Q ⊃ R 5. ~L/ ~R 6. Q ⊃ SHypothetical Syllogism 1, 4 7. ~PModus Ponens 2, 6 8. (Q ⊃ R) ⊃ (L v ~S)Modus Ponens, 3, 7 9. L v ~SModus Ponens 4, 8 10. ~SModus Tollens 5, 9 11. ~QDisjunctive Syllogism 6, 10 12. ~RDisjunctive Syllogism 4, 11

Analyze each proof.  Decide if the proof is correct, or if the proof has an error. Inelegant proofs are not necessarily incorrect. 1. P 2. (Q ⊃ R) ⊃ (P ⊃ Q) 3. P ⊃ (Q ⊃ R)/ R 4. Q ⊃ RModus Ponens 1, 3 5. P ⊃ QModus Ponens 2, 4 6. P ⊃ RHypothetical Syllogism 4, 5 7. RModus Ponens 1, 6

Analyze each proof.  Decide if the proof is correct, or if the proof has an error. Inelegant proofs are not necessarily incorrect. 1. ~R v (P ⊃ Q) 2. (P ⊃ Q) ⊃ (Q ⊃ ~R) 3. ~~R/ ~P 4. P ⊃ QDisjunctive Syllogism 1, 3 5. Q ⊃ ~RModus Ponens 2, 4 6. ~QModus Tollens 3, 5 7. ~PModus Tollens 4, 6

     Consider the following argument: No environmentally produced diseases are inherited afflictions. Some psychological disorders are not inherited afflictions. Therefore, some psychological disorders are environmentally produced diseases.      What is the figure of this argument?

Determine a correct contradiction to the following statements.  If Biden wins, then if Harris is vice-president then Pence is not vice-president.