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Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA Q&E ~Q&E
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA Q & ~Q E Q&E ~Q&E
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA ~B Q & ~Q E Q&E ~Q&E
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA ~B E Q & ~Q E Q&E ~Q&E
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA A v ~C ~B E Q & ~Q E Q&E ~Q&E
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA A v ~CvI ~B E Q & ~Q E Q&E ~Q&E
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA 4 A3 &E A v ~CvI ~B E Q & ~Q E Q&E ~Q&E
Show that {(A v ~C) ~B, [~B (Q &~Q)], ~C & A} ⊦ is inconsistent in SD 1 (A v ~C) ~BA 2 ~B (Q & ~Q)A 3 ~C & AA 4 A3 &E 5 A v ~C4 vI 6 ~B 1, 5 E 7 Q & ~Q 6, 2 E 8 Q7 &E 9 ~Q7 &E
Show that [A (B C)] [(A & B) C] is a theorem in SD. [A (B C)] [(A & B) C]
Show that [A (B C)] [(A & B) C] is a theorem in SD. A (B C) A/ I (A & B) C [A (B C)] [(A & B) C] I
Show that [A (B C)] [(A & B) C] is a theorem in SD. A (B C) A/ I A & B A/ I C (A & B) C I [A (B C)] [(A & B) C] I
Show that [A (B C)] [(A & B) C] is a theorem in SD. A (B C) A/ I A & B A/ I B C C E (A & B) C I [A (B C)] [(A & B) C] I
Show that [A (B C)] [(A & B) C] is a theorem in SD. A (B C) A/ I A & B A/ I B C E C E (A & B) C I [A (B C)] [(A & B) C] I
Show that [A (B C)] [(A & B) C] is a theorem in SD. A (B C) A/ I A & B A/ I A &E B C E C E (A & B) C I [A (B C)] [(A & B) C] I
Show that [A (B C)] [(A & B) C] is a theorem in SD. A (B C) A/ I A & B A/ I A 2 &E B C 1,3 E B 2 &E C E (A & B) C I [A (B C)] [(A & B) C] I
Show that [A (B C)] [(A & B) C] is a theorem in SD. 1 A (B C) A/ I 2 A & B A/ I 3 A 2 &E 4 B C 1,3 E 5 B 2 &E 6 C 4,5 E 7 (A & B) C 2-6 I 8 [A (B C)] [(A & B) C] 1-7 I
Show that A ~B and B ~A are equivalent in SD A ~BA B ~A
Show that A ~B and B ~A are equivalent in SD 1 A ~BA 2 BA/ I ~A B ~A I
Show that A ~B and B ~A are equivalent in SD 1 A ~BA 2 BA/ I 3 A A/~I ~A~I B ~A I
Show that A ~B and B ~A are equivalent in SD 1 A ~BA 2 BA/ I 3 A A/~I 4 B2 R 5 ~B 1,3 E ~A~I B ~A I
Show that A ~B and B ~A are equivalent in SD 1 A ~BA 2 BA/ I 3 A A/~I 4 B2 R 5 ~B 1,3 E 6 ~A3-5 ~I 7 B ~A1-6 I
Show that A ~B and B ~A are equivalent in SD Here is the other derivation (you need both). 1 B ~AA 2 AA/ I 3 B A/~I 4 A2 R 5 ~A 1,3 E 6 ~B3-5 ~I 7 A ~B1-6 I
Show that (~A B) (A ~B) is a theorem in SD. (~A B) (A ~B)
Show that (~A B) (A ~B) is a theorem in SD. 1 ~A BA/ I A ~B (~A B) (A ~B) I
Show that (~A B) (A ~B) is a theorem in SD. 1 ~A BA/ I A ~B I (~A B) (A ~B) I
Show that (~A B) (A ~B) is a theorem in SD. 1 ~A BA/ I 2 AA/ I ~ B ~BA/ I A A ~B I (~A B) (A ~B) I
Show that (~A B) (A ~B) is a theorem in SD. 1 ~A BA/ I 2 AA/ I ~ B ~I ~BA/ I A~E A ~B I (~A B) (A ~B) I
Show that (~A B) (A ~B) is a theorem in SD. 1 ~A BA/ I 2 AA/ I 3 BA/~I 4 A2R 5 ~A1, 3 E 6 ~B 3-5 ~I 7 ~BA/ I A8-10~E A ~B2-6, 7-11 I (~A B) (A ~B)1-12 I
Show that (~A B) (A ~B) is a theorem in SD. 1 ~A BA/ I 2 AA/ I 3 BA/~I 4 A2R 5 ~A1, 3 E 6 ~B 3-5 ~I 7 ~BA/ I 8 ~AA/~E 9. ~B7R 10. B1, 8 E 11 A8-10~E 12 A ~B2-6, 7-11 I 13 (~A B) (A ~B)1-12 I
Show that the following argument is valid in SD: (A v C) v B (A v B) v (B v C) 1 (A v B) v BA (A v B) v (B v C)
Show that the following argument is valid in SD: (A v C) v B (A v B) v (B v C) 1 (A v B) v BA (A v B) v (B v C)vE
Show that the following argument is valid in SD: (A v C) v B (A v B) v (B v C) 1 (A v C) v BA 2 A v CA/vE (A v B) v (B v C)1, BA/vE (A v B) v (B v C) (A v B) v (B v C)1, vE
Show that the following argument is valid in SD: (A v C) v B (A v B) v (B v C) 1 (A v C) v BA 2 A v CA/vE (A v B) v (B v C)1, BA/vE A v BvI (A v B) v (B v C)vI (A v B) v (B v C)1, vE
Show that the following argument is valid in SD: (A v C) v B (A v B) v (B v C) 1 (A v C) v BA 2 A v CA/vE 3 AA/vE 4 A v B3, vI 5 (A v B) v (B v C)4, vI 6 CA/vE 7 B v C 6 vI 8 (A v B) v (B v C)7 vI 9 (A v B) v (B v C)2, 3-5, 6-8 vE 10 BA/vE 11 A v B10 vI 12 (A v B) v (B v C)11 vI 13 (A v B) v (B v C)1, 2-9, vE