LESSON #14: PRACTICE WITH PROOFSThis lesson provides seven different proof problems for practice using the proof rules we’ve learned so far. We probably won’t have time to cover them all in class, so be sure to think through on your own the ones we don’t get to, using the solutions below as your guide.POWERPOINT SLIDES #1-5 Problem requires both conjunction rules and ᴠ Intro:(The powerpoint slides provide commentary walking you through each step of the proof.)1 Tet(a) ᴧ Large(a)2 Med(b) ᴧ Dodec(b)3 Large(a) ᴧ Elim: 14 Dodec(b) ᴧ Elim: 2 5 Large(a) ᴧ Dodec(b) ᴧ Intro: 3,4 6 (Large(a) ᴧ Dodec(b)) ᴠ Cube(c) ᴠ Intro: 5Fitch problem 6.3 Problem requires both conjunction rules and =Elim:1 a = b ∧ b = c ∧ c = d2 a = b ᴧ Elim: 13 b = c ᴧ Elim: 14 a = c = Elim: 2,35 c = d ᴧ Elim: 16 b = d = Elim: 3,57 a = c ᴧ b = d ᴧ Intro: 4,6POWERPOINT SLIDES #6-12 Problem requires ᴧ Elim and both disjunction rules(The powerpoint slides provide commentary walking you through each step of the proof.)1 (A ᴧ B) ᴠ (C ᴧ D)2 A ᴧ B3 B ᴧ Elim: 24 B ᴠ D ᴠ Intro: 3 5 C ᴧ D 6 D ᴧ Elim: 57 B ᴠ D ᴠ Intro: 68 B ᴠ D ᴠ Elim: 1, 2-4, 5-7Fitch problem Proof Disjunction 2 Problem requires ᴧ Intro and both disjunction rules1 Cube(b)2 Small(b) ᴠ Large(b)3 Small(b)4 Cube(b) ᴧ Small(b) ᴧ Intro: 1,35 (Cube(b) ᴧ Small(b) ᴠ (Cube(b) ᴧ Large(b)) ᴠ Intro: 46 Large(b) 7 Cube(b) ᴧ Large(b) ᴧ Intro: 1,68 (Cube(b) ᴧ Small(b) ᴠ (Cube(b) ᴧ Large(b)) ᴠ Intro: 79 (Cube(b) ᴧ Small(b) ᴠ (Cube(b) ᴧ Large(b)) ᴠ Elim: 2, 3-5, 6-8Fitch problem 6.4 Problem again requires ᴧ Elim and both disjunction rules1 (A ᴧ B) ᴠ C2 A ᴧ B3 B ᴧ Elim: 24 C ᴠ B ᴠ Intro: 35 C6 C ᴠ B ᴠ Intro: 57 C ᴠ B ᴠ Elim: 1, 5-6, 2-4Fitch problem 6.5 Problem requires both conjunction rules and both disjunction rules (and provides an example of needing to make a disjunction accessible first before it is available to use as basis of a disjunction elimination strategy)1 A ᴧ (B ᴠ C)2 A ᴧ Elim: 13 B ᴠ C ᴧ Elim: 14 B5 A ᴧ B ᴧ Intro: 2,46 (A ᴧ B) ᴠ (A ᴧ C) ᴠ Intro: 57 C8 A ᴧ C ᴧ Intro: 2,79 (A ᴧ B) ᴠ (A ᴧ C) ᴠ Intro: 810 (A ᴧ B) ᴠ (A ᴧ C) ᴠ Elim: 3, 4-6, 7-9Fitch problem 6.6 Problem requires both conjunction rules and both disjunction rules (and provides an example of more than one ‘common conclusion’ can bereached in the same two subproofs and used with two separate applications of disjunction elimination)1 (A ᴧ B) ᴠ (A ᴧ C)2 A ᴧ B3 A ᴧ Elim: 24 B ᴧ Elim: 25 B ᴠ C ᴠ Intro: 46 A ᴧ C 7 A ᴧ Elim: 68 C ᴧ Elim: 69 B ᴠ C ᴠ Intro: 810 A ᴠ Elim: 1, 2-5, 6-911 B ᴠ C ᴠ Elim: 1, 2-5, 6-912 A ᴧ (B ᴠ C) ᴧ Intro:
View Full Document
Unlocking...