Hello, I need help writing proofs for a logic and moral reasoning philosophy class. The proofs are for: 1. Premises: q -> (q &~ q) Conclusion: ~q 2. Premises: k & l
PHI 1600 Spring 2021 (1) Premises: q -> (q &~ q) Conclusion: ~q (2) Premises: k & l Conclusion: (k – > l) & (l -> k) (3) Premises: p & (q V r), p -> ~r Conclusion: q V e (4) Premises: ~(p -> q) Conclusion: ~q (5) Premises: (a V b) & (c V d), a -> (e -> (c &d)), c <-> ~d Conclusion: e -> b
Hello, I need help writing proofs for a logic and moral reasoning philosophy class. The proofs are for: 1. Premises: q -> (q &~ q) Conclusion: ~q 2. Premises: k & l
HW 7 Create proofs for each problem that start with the premises given and end with the given conclusion. (1) Premises: p & q Conclusion: p V q p & q Simp, 1 p V q Add 2 (2) Premises: Conclusion: (p V q) V r p p V q Add, 1 (p V q) V r Add, 2 (3) Premises: p -> q Conclusion: q V r p -> q MP, 1-2 q V r Add, 3 (4) Premises: p & (q & r) r -> s Conclusion: p & (q & r) r -> s q & r Simp, 1 Simp, 2 MP, 2, 4 (5) Premises: q (p & q) -> r Conclusion: p (p &q) -> r p & q Conj 1, 2 MP 3, 4
Hello, I need help writing proofs for a logic and moral reasoning philosophy class. The proofs are for: 1. Premises: q -> (q &~ q) Conclusion: ~q 2. Premises: k & l
HW 9 Write proofs for the following problems. (1) Premises: g -> (~o -> (g -> d)) o V g ~o Conclusion: g -> (~o -> (g -> d)) o V g ~o DS 2, 3 ~o -> (g -> d) MP 1, 4 6. g -> d MP 5, 3 7. d MP 6, 4 (2) Premises: (u & (~(~p))) -> q ~o -> u ~p -> o ~o & t Conclusion: q 1. (u & (~(~p))) -> q A 2. ~o -> u A 3. ~p -> o A 4. ~o & t A 5. ~o Simp 4 6. u MP 2, 5 7. ~~p MT 3, 5 8. u & ~~p Conj 6, 7 9. q MP 1, 8 (3) Premises: m -> (u -> h) (h V ~u) -> f Conclusion: m -> f 1. m -> (h V ~u) 2. (h V ~u) -> f –3. m CA –4. u -> h MP 1, 3 –5. ~u V h MI 4 –6. h V ~u Commut 5 –7. f MP 2, 6 8. m -> f CP 3-7 (4) Premises: (i -> e) -> c c -> ~c Conclusion: 1. (i -> e) -> c A 2. c -> ~c 3. ~c V ~c MI 2 4. ~c Taut 3 5. ~(i -> e) MT 1, 4 6. ~(~i V e) MI 5 7. ~~i & ~e DM 8. ~~i Simp 7 9. i DN 8 (5) Premises: i -> ~(g V f) ~t V i Conclusion: ~f 1. i -> ~(g V f) 2. ~t V i 3. t 4. ~~t DN 3 5. i DS 2, 4 6. ~(g V f) MP 1, 5 7. ~g & ~f DM 6 8. ~f Simp 7
Hello, I need help writing proofs for a logic and moral reasoning philosophy class. The proofs are for: 1. Premises: q -> (q &~ q) Conclusion: ~q 2. Premises: k & l
HW 10 Write proofs for the following problems. (1) Premises: a -> b a -> c b -> ~c Conclusion: ~a 1. a -> b A 2. a -> c 3. b -> ~c -4. a SA -5. c MP 2, 4 -6. b MP 1, 4 -7. ~c MP 3, 6 -8. c & ~c Conj 5, 7 9. ~a IP 4-8 (2) Premises: ~(p V q) (~r) -> (~s) r -> (q V ~s) ~(p V q) (~r) -> (~s) r -> (q V ~s) -4. s SA -5. ~~s DN 4 -6. ~~r MT 2, 5 -7. r DN 6 -8. q V ~s MP 3, 7 -9. q DS 8, 5 -10. p V q Add 9 -11. (p V q) & ~(p V q) Conj 10, 1 12. ~s IP 4 (3) Premises: (~q) <-> (~p) (r <-> s) V ((r & s) V (~r & ~s)) (~r) V p s V ~q Conclusion: (~q) <-> (~p) (r <-> s) V ((r & s) V (~r & ~s)) (~r) V p s V q ((r & s) V (~r & ~ s)) V ((r & s) V (~r & ~s)) ME 5 (r & s) V (~r & ~s) Taut 6 -8. ~r & ~s SA -9. ~s Simp 8 -10. s & ~s Conj 5, 9 11. ~(~r & ~s) IP 8-10 12. r & s DS 7, 11 13. r Simp 12 14. ~~r DN 13 15. p Ds 3, 14 (4) Premises: p -> q q -> r Conclusion: p -> (q & r) p -> q q -> r -3. P SA -4. q MP 1, 3 -5.r MP 2, 4 -6. q & r Conj 4, 5 7. p -> (q & r) CP 3-6 (5) Premises: y -> (z V w) ~w (~z) V x Conclusion: (~x) -> (~y) y -> (z V w) ~w (~z) V x -4. y SA -5. z V w MP 1, 4 -6. z DS 5, 2 -7. ~~z DN 6 -8. x DS 3, 7 9. y -> x CP 4-8 10. ~x -> ~y Trans 9 (6) Premises: ~(a & b) b V c Conclusion: a -> c ~(a & b) b V c -3. a SA -4. ~a V ~b DM 1 -5. ~~a DM 3 -6. ~b DS 4, 5 -7. c DS 2, 6 8. a ->c CP 3-7 (7) Premises: x -> y ((~y) V z) & ((~y) V w) Conclusion: x -> z x -> y ((~y) V z) & ((~y) V w) -3. x SA -4. y MP 1, 3 -5. ~y V z Simp 2 -6. ~~y DN 4 -7. z DS 5, 6 x -> z CP 3-7
Hello, I need help writing proofs for a logic and moral reasoning philosophy class. The proofs are for: 1. Premises: q -> (q &~ q) Conclusion: ~q 2. Premises: k & l
HW 11 Write proofs for the following problems. (2) Premises: x -> (y & z) y -> (w & ~w) ~x -> w Conclusion: x -> (y & z) y -> (w & ~w) ~x -> w -4. ~w SA -5. ~~x MT 3, 4 -6. x DN 5 -7. y & z MP 1, 6 -8. y Simp 7 -9. w & ~w MP 2, 8 10. ~~w IP 4-9 11. w DN 10 (4) Premises: (~a) -> ((b & c) V (b & d)) ~(e V b) Conclusion: (~a) -> ((b & c) V (b & d)) ~(e V b) -3. ~a SA -4. (b & c) V (b & d) MP 1, 3 -5. ~e & ~b DM 2 -6. ~b Simp 5 –7. b & c SA –8. b Simp 7 –9. b & ~b Conj 8, 6 -10. ~(b & c) IP 7-9 –11. b & d SA –12. b Simp 11 –13. b & ~b Conj 12, 6 -14. ~(b & d) IP 11-13 -15. ~(b & c) & ~(b & d) Conj 10, 14 -16. ~((b & c) V (b & d)) DM 15 -17. ((b & c) V (b & d)) & ~((b & c) V (b & d)) Conj 4, 16 18. ~~a IP 3-17 19. a DN 18 ~(p & q) ~(p V q) ________ _______ ~p V ~q ~p &~q (6) Premises: (x V y) & (x V z) z -> w ~(w & z) Conclusion: (x V y) & (x V z) z -> w ~(w & z) -4. ~x SA -5. x V z Simp 1 -6. z DS 5, 4 -7. w MP 2, 6 -8. ~w V ~z DM 3 -9. ~~w DN 7 -10. ~z DS 8, 9 -11. z & ~z Conj 6, 10 12.~~x IP 4-11 13. x DN 12 (8) Premises: b V (~c) (~c) -> (~a) Conclusion: (~a) V b b V (~c) (~c) -> (~a) -3. a SA -4. ~~a DN 3 -5. ~~c MT 2, 4 -6. b DS 1, 5 7. a -> b CP 3-6 8. ~a V b MI 7 (10) Premises: p <-> q Conclusion: (~p) <-> (~q) p <-> q (p -> q) & (q -> p) ME 1 p -> q Simp 2 q -> p Simp 2 -5. ~p SA -6. ~q MT 4, 5 7. ~p -> ~q CP 5-6 -8. ~q SA -9. ~p MT 4, 5 10. ~q -> ~p CP 8-9 -11. (~p -> ~q) & (~q -> ~p) Conj 7, 9 12. ~p <-> ~q ME 11 (12) Premises: p -> q r V p ~(q & r) Conclusion: p <-> q p -> q r V p ~(q & r) -4. q SA -5. ~q V~r DM 3 -6. ~~q DN 4 -7. ~r DS 5, 6 -8. p DS 2, 7 9. q -> p CP 4-8 10. (p -> q) & (q -> p) Conj 1, 9 11. p <-> q ME 10