SOLUCIÓN EJERCICIOS CON REGLAS DERIVADAS Y REDUCCIÓN AL ABSURDO
PRIMERO: |--- Ø p
- -1 Ø (p Ù q)
- -2 p ® r
- -3 q Ú
Ø r
- 4 p [Premisa subsidiaria]
- 5 r [MP 2,3]
- 6 q [TP 3,5]
- 7 (Ø p Ú
Ø q) [DM 1]
- 8 Ø q [TP 7,4]
- 9 q Ù
Ø q [IC 6,8]
- 10 Ø p [Abs 4-9]
SEGUNDO: |--- Ø T
- -1 T ® Ø S
- -2 F ®
Ø T
- -3 S Ú F
- 4 T [Premisa subsidiaria]
- 5 Ø S [MP 1,4]
- 6 F [TP 3,5]
- 7 Ø T [MP 2,6]
- 8 T Ù
Ø T
- 9 Ø T [Abs 4-8]
TERCERO: |--- r
- -1 Ø
(p Ù q)
- -2 Ø r
® q
- -3 Ø p
® r
- 4 Ø r [Premisa subsidiaria]
- 5 q [MP 2,4]
- 6 Ø
Ø p [MT 3,4]
- 7 p [DN 6]
- 8 p Ù q [IC 7,5]
- 9 (p Ù q)
Ù Ø
(p Ù q) [IC 8,1]
- 10 Ø r [Abs 4-9]
CUARTO: |--- Ø
(A Ù D)
- -1 A ®
(B Ú C)
- -2 B ® ØA
- -3 D ®
Ø C
- 4 A Ù D [Premisa subsidiaria]
- 5 A [EC 4]
- 6 B Ú C [MP 1,5]
- 7 D [EC 5]
- 8 Ø C [MP 3,7]
- 9 B [TP 6,8]
- 10 Ø A [MP 2-9]
- 11 Ø B [MT 2-5]
- 12 Ø A
Ù
Ø B [IC 10,11]
- 13 Ø (A Ú B) [DM 12]
- 14 (A Ú B)[ID 5]
- 15 (A Ú B)
Ù Ø
(A Ú B) [IC 14,13]
- 16 Ø
(A Ù D)[Abs 4-15]
QUINTO: |--- Ø E Ú M
- -1 S Ú O
- -2 S ®
Ø E
- -3 O ® M
- 4 Ø (Ø E Ú M )[Premisa Subsidiaria]
- 5 (Ø
Ø E Ù
ØM) [DM 4]
- 6 Ø M [EC 5]
- 7 Ø O [MT 3,6]
- 8 S [TP 1,7]
- 9 Ø E [MP 2,8]
- 10 (Ø E Ú M) [ID 9]
- 11 (Ø E Ú M ) ÙØ (Ø E Ú M ) [IC 10-4]
- 12 Ø E Ú M [Abs 4-11]
SEXTO: |--- Ø t
- -1 p Ú q
- -2 t ®
Ø p
- -3 Ø
(q Ú r)
- 4 t [Premisa Subsidaria]
- 5 Ø p [MP 2,4]
- 6 q [TP 1,5]
- 7 q Ú r [ID 6]
- 8 (q Ú r)
Ù
Ø
(q Ú r) [IC 7,3]
- 9 t [Abs 4-8]
SEPTIMO: |--- Ø (t Ú s)
- -1 Ø R
Ú Ø B
- -2 (T Ú S)
® R
- -3 B Ú
Ø S
- -4 Ø T
- 5 T Ú S [Premisa Subsidiaria]
- 6 R [MP 2,5]
- 7 Ø B [TP 1,6]
- 8 Ø S [TP 3,7]
- 9 T [TP 5,8]
- 10 T Ù Ø T [IC 9,4]
- 11 Ø (T Ú S)[Abs 5-10]
OCTAVO: |--- Ø p
- -1 p ®
Ø s
- -2 s Ú
Ø r
- -3 Ø
(t Ú Ø r)
- 4 p [Premisa Subsidaria]
- 5 Ø s [MP 1,4]
- 6 Ø r [TP 2,5]
- 7 t Ú
Ø r [ID 6]
- 8 (t Ú
Ø r)
Ù Ø
(t Ú
Ø r) [IC 7,3]
- 9 Ø p [Abs 4-8]
NOVENO: |--- Ø s
Ú
Ø t
- -1 Ø p
®
Ø s
- -2 Ø p
Ú r
- -3 r ®
Ø t
- 4 Ø
(Ø s
Ú
Ø t) [Premisa Subsidiaria]
- 5 s Ù t [DM 4]
- 6 s [EC 5]
- 7 p [MT 1,6]
- 8 r [TP 2,3]
- 9 Ø t [MP 3,8]
- 10 t [EC 5]
- 11 t Ù
Ø t [IC 10,9]
- 12 Ø s
Ú
Ø t [Abs 4-11]
DECIMO: |--- s Ú r
- -1 Ø r
®
p Ú q
- -2 Ø
( Ø p
Ú r)
® s
- -3 Ø p
®
Ø q
- 4 Ø
( s Ú r )[Premisa Subsidiaria]
- 5 (Ø s
Ù
Ø r) [DM 4]
- 6 Ø s [EC 5]
- 7 Ø
Ø(Ø
p Ú r ) [MT 2,6]
- 8(Ø
p Ú r ) [DN 7]
- 9 Ø r [EC 5]
- 10 Ø p [TP 8,9]
- 11 Ø q [MP 3,10]
- 12 Ø p
Ù
Ø q) [IC 10,11]
- 13 Ø
(p Ú q) [DM 12]
- 14 Ø
Ø r [MT 1,13]
- 15 r [DN 14]
- 16 (r Ù
Ø r) [IC 15,9]
- 17 s Ú r [Abs 4-16]
UNDECIMO: |--- Ø
(p Ù
Ø
(p Ù q)
- -1 r ® t
- -2 t ®
Ø s
- -3 (r ®
Ø s)
® q
- 4 (p Ù
Ø
(p Ù q) [Premisa Subsidiaria]
- 5 Ø
(p Ù q) [EC 4]
- 6 (Ø
p Ú
Ø q)[DM 5]
- 7 p [EC 4]
- 8 Ø q [TP 6,7]
- 9 Ø
( r ® s) [MT 3,8]
- 10 r ®
Ø s [Sil 1,2]
- 11( r ®
Ø s)
Ù
Ø
( r ®
Ø s) [IC 10,9]
- 12 Ø
(p Ù
Ø
(p Ù q) [Abs 4-11]
DUODECIMO: |--- Ø
(t Ú s)
- -1 Ø r
Ú
Ø q
- -2 (t Ú s)
® r
- -3 (q Ú
Ø s)
- -4 Ø t
- 5 t Ú s [Premisa Subsidiaria]
- 6 s [MT 4,5]
- 7 r [MP 2,5]
- 8 Ø q [TP 1,7]
- 9 Ø s [TP 3,8]
- 10 s Ù
Ø s [IC 6,9]
- 11 Ø
(t Ú s) [Abs 5-10]
DECIMOTERCERO: |--- Ø
(s Ù
Ø r)
- -1 p ®
Ø q
- -2 r ®
Ø s
- -3 q Ù r
- -4 p Ú r
- 5 Ø q
Ú
Ø s [Dil 4,1,2]
- 6 q [EC 3]
- 7 Ø s [TP 5,6]
- 8 Ø s
Ú r [ID 7]
- 9 Ø
(Ø
Ø s
Ù
Ø r) [DM 8]
- 10 Ø
( s Ù
Ø r [DN 9]
DECIMOCUARTO: |--- Ø
(q Ù r)
- -1 p ®
Ø q
- -2 Ø
(r Ù
Ø p)
- 3 q Ù r [Premisa Subsidiaria]
- 4 q [EC 3]
- 5 Ø p [MT 1,4]
- 6 Ø r
Ú
Ø
Ø p [DM 2]
- 7 Ø r [TP 6,5]
- 8 r [EC 3]
- 9 r Ù
Ø r [IC 8,7]
- 10 Ø
(q Ù r) [Abs 3-9]
DECIMOQUINTO: |--- r Ú s
- -1 p Ú
Ø(
Ø q
Ù
Ø r)
- -2 Ø p
Ù
Ø q
- 3 Ø
( r Ú s)[Premisa Subsidiaria]
- 4 Ø p [EC 2]
- 5 Ø
( Ø q
Ú
Ø r)[TP 1,4]
- 6 q Ù r [DM 5]
- 7 Ø q [EC 2]
- 8 q [EC 6]
- 9 q Ù
Ø q [IC 8,7]
- 10 r Ú s [Abs 3-9]
DECIMOSEXTO: |--- Ø
( Ø q
Ù
Ø t)
- -1 s ® r
- -2 s Ú p
- -3 p ® q
- -4 r ® t
- 5 Ø q
Ù
Ø t [Premisa Subsidiaria]
- 6 r Ú q [Dil 2,1,3]
- 7 Ø q [EC 5]
- 8 Ø p [MT 3,7]
- 9 s [TP 2,8]
- 10 s ® t [Sil 1,4]
- 11 t [MP 10,9]
- 12 Ø t [EC 5]
- 13 t Ù
Ø t [IC 11,12]
- 14 Ø
( Ø q
Ù
Ø t) [Abs 5-13]
Ejercicios Derivadas por Absurdo