1 / 10

A v B ~ A

A v B ~ A. B > C ~C. B > (C . P) B. / ~ B mt 1,2. / B ds 1,2. / C . P mp 1,2. ~~S R > ~S. A v B C > D. / ~ R mt 1,2. / (A v B) . (C > D) cn 1,2. A > (B. C) (B . C) > K . 1. (L > M) . (D v N). / L > M sm 1. / A > K hs 1,2. R . T premise

gus
Download Presentation

A v B ~ A

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A v B • ~ A • B > C • ~C • B > (C . P) • B / ~ B mt 1,2 / B ds 1,2 / C . P mp 1,2 • ~~S • R > ~S • A v B • C > D / ~ R mt 1,2 / (A v B) . (C > D) cn 1,2 • A > (B. C) • (B . C) > K 1. (L > M) . (D v N) / L > M sm 1 / A > K hs 1,2

  2. R . T premise • R > S premise • R ___ • S ___ 1 sm 2,3 mp • B > P premise • P > X premise • B > X ___ • (B > X) . (B > P) ___ 1,2 hs 3,1 cn

  3. ~ (A > P) > ~S premise • S premise • ~~S ___ • ~~ (A > P) ___ • A > P ___ 2, dn 1,3 mt 4, dn • (D v S) > (P . Q) premise • S v D premise • D v S ___ • P . Q ___ • Q . P ___ • Q ___ 2, cm 3,1 mp 4, cm 5 sm

  4. P . (Q . R) premise • (P . Q) . R ___ • R . (P . Q) ___ • R ___ 1, as 2, cm 3 sm • S > (A . (B v C)) premise • S premise • A . (B v C) ___ • B v C ___, ___ 1,2 mp 3, cm , sm • (L v X) > (A . B) premise • M premise • M > (X v L) premise • (X v L) > (A . B) ___ • M > (A . B) • A . B ___ • A ___ • B ___ 1 cm 3,4 hs 2,5 mp 6 sm 6 cm, sm

  5. J > (K > L) premise • L v J premise • ~L premise • J ___ • K > L ___ • ~K ___ 2,3 ds 1,4 mp 3,5 mt • ~G > ( G v (S > G)) premise • (S v L) > ~G premise • S v L premise • ~ G ___ • G v (S > G) ___ • S > G ___ • ~S ___ • L ___ 2,3 mp 1,4 mp 4,5 ds 4,6 mt 3,7 ds

  6. (K . B) v ( ~L > E) • ~( B . K) • ~E / L • (K . O) > (N v T) • O • K / T v N • (R > F) > ((R > ~G) > (S > Q)) • (Q > F) > (R > Q) • ~G > F • Q > ~G / S > F If a tenth planet exists, its orbit is perpendicular to that of the other planets. Either a tenth planet is responsible for the death of the dinosaurs or its orbit is not perpendicular to that of the others. A tenth planet is not responsible for the death of the dinosaurs, so there is no tenth planet.

  7. How do you approach doing a proof? First, you look to see if the conclusion –at least a piece of it—can be located in one of the premises: here you spot it in line 1, as the consequent. Unfortunately, the order of the letters is wrong. But that tells us two things: Commutation will be the final step of the proof; and MP will be the one before that. How do we know? 1. (K . O) > (N v T) 2. O 3. K / T v N Because MP is the rule that delivers a consequent, and CM is the rule that switches the order of letters around dots and wedges. 4. K . O CN 2,3 5. N v T MP 4, 1 6. T v N CM 5

  8. 1. (K . B) v ( ~L > E) 2. ~( B . K) 3. ~E / L Find the conclusion in the premise: It’s in line 1, but it’s negated! Not only that, but it’s in the location of an antecedent. Negated antecedent? Sounds like MT. Can we use line 3 with line 1 to get ~~L (which is equivalent to L by DN)? No! MT –and all the rules of inference—only works at the main operator of a line; the main operator of 1 is a wedge. You’ll have to use DS to break the right-hand disjunct out of 1 and put it on a line by itself. To that line you could do MT. CM will change the order of B and K; you can either change line 1 or change line 2 –one of them has to be changed so that they match up exactly for DS.

  9. 1. (K . B) v ( ~L > E) 2. ~( B . K) 3. ~E / L 4. ~( K . B) CM 2 5. ~L > E DS 1,4 6. ~~L MT 5,3 7. L DN 6

  10. If you don’t start out by looking for the conclusion –or a piece of it at least– in the premises, then you are just guessing. As you might expect, if you are just guessing, it’s just a matter of luck. That’s not how to succeed in Logic, though.

More Related