PHILOSOPHY 102
1. The maid remained in her quarters on the night of the crime. If the butler committed the crime, then either the maid is an accomplice or the stolen gems are still in the mansion. If the stolen gems are still in the mansion, the maid
RULES OF INFERENCE
Modus Ponens (MP) p p q q Modus Tollens (MT) p q p q Conjunction (Conj) p q p q
Hypothetical Syllogism (HS) p q p q r r
Simplification (Simp) p q p p q q
Constructive Dilemma (CD) p r q s
pvr qvs
Disjunctive Syllogism (DS) pvq
1. A (B C) ~C/ ~A ~B 2. C (BD) B E C/ E 3. M (BD) ~B/ M 4. A B B C/
16. A B ~A ~A (HL) (HB) (BH) K / K 17. ~ K N (JK) L (J L) M / K (MN) 18. A C (B C) (DE) / A (B
31. ~ A B ~ A ( ~ B C) / ~AvC 32. A B B C/ A (AC)
33. ~ T v [(U v W) V] / T (U V)
1. A (B C) ~C/ ~A ~B 2. C (BD) B E C/ E 3. M (BD) ~B/ M 4. A B B C/
16. A B ~A ~A (HL) (HB) (BH) K / K 17. ~ K N (JK) L (J L) M / K (MN) 18. A C (B C) (DE) / A (B
31. ~ A B ~ A ( ~ B C) / ~AvC 32. A B B C/ A (AC)
33. ~ T v [(U v W) V] / T (U V)
Philosophy 102 Homework Sheet I
1. p (q r) pvq p r
8.
p q r t u
q (r s) t u p
15.
A C A B
B D C D
2.
p q p
q r r 9. (p p s s q) r
16.
AvB Av A
(H L) v (H B) (B H) K K
3.
p r r
(q p q
r)
r
10.
p
(q r) t
17.
KvN (J (J K) K L) L M
PHILOSOPHY 102
1. The maid remained in her quarters on the night of the crime. If the butler committed the crime, then either the maid is an accomplice or the stolen gems are still in the mansion. If the stolen gems are still in the mansion, the maid