Más ejercicios de lógica

EJERICICOS DE LÓGICA

1 EC, ID, DN, IC	-1 (s -> t) & (r & t) I- (s -> t) & r
2 EC, ID, DN, IC	-1 (p & q) & (r & s) I- p & r
3 EC, ID, DN, IC	-1 (p -> q) & ¬¬ (r v q) I- (p -> q) & ( r v s)
4 EC, ID, DN, IC	-1 p & (q & r) I- (p & q) & r
5 MP	-1. t -> q -2. s v r -> v -3. v & q -> p -4. t & s I- p
6 IB	-1. p v q -> (q -> p & q) -2. r & (p & q -> q) -3. ¬¬p I- q <-> p & q
7 IB	-1. p & ¬¬(q -> r) -2. r -> q I- q <-> r
8 EB	-1. p <-> q -2. r <-> (p & q) -3. ¬¬p I- r v s
9 EB	-1. p <-> t -2. ¬s <-> t -3. ¬¬ (t -> ¬s) <-> ¬¬q -4. p I- p & q
10 IN	-1 p & q -> r -2 r -> s -3 q & ¬s I- ¬p
11 IN	-1 q & (r <-> q) -2 ¬ r -> p I- ¬ r
12 IC	-1 t -> q -2 w -> r -3 r & q -> p I- t & w -> p
13 IC	-1 p -> r -2 ¬ (q -> r) I- ¬ (q -> p)
14 IC	-1 p -> (q -> r) -2 s -> p & q I- ¬¬s -> r
15 IC	-1 p & q -> r I- p -> (q -> r)
16 ED (144)	- 1 ¬q -> r - 2 t -> ¬ q - 3 ¬ s -> ¬ q I-t v ¬s -> r
17 ED	-1 p -> q -2 r -> p -3 t -> r -4 s -> r -5 t v s I- q v ¬w
18 ED	-1 p & (q v r) I- (p & q) v (p & r)
19 ED	-1 (p v q) v r I- p v (q v r)
20 REGLAS BÁSICAS	-1 q -> ¬p -2 r -> q -3 r I- ¬p
21 REGLAS BÁSICAS	-1 ¬ p -> ¬ q -2 s v ¬q -> ¬¬ r -3 ¬p I- r
22 REGLAS BÁSICAS	-1 p <-> ¬¬ (q & r) -2 q & (r -> s) -3 p I- s
23 REGLAS BÁSICAS	-1 ¬p <-> q -2 s v t -> ¬p -3 ¬¬ s I- q v r
24 REGLAS BÁSICAS	-1 p -2 p -> ¬ q -3 p & ¬q -> ¬¬s -4 s -> ¬¬ t I- t
25 REGLAS BÁSICAS	-1 p -2 p -> q -3 ¬¬( q -> ¬ s) I- ¬s
26 REGLAS DERIVADAS	-1 p -> q I- ¬q -> ¬p
27 REGLAS DERIVADAS	-1 ¬ p -> ¬q -2 q I- p
28 REGLAS DERIVADAS	-1 q & r -> ¬s -2 s I- ¬q v ¬r
29 REGLAS DERIVADAS	-1 p -> q & r -2 ¬ q v ¬ r I- ¬p
30 REGLAS DERIVADAS	-1 p v q -> r -2 ¬ r I- ¬q
31 REGLAS DERIVADAS	-1 ¬ p -2 q -> p -3 ¬q -> r I- r v s
32 REGLAS DERIVADAS	-1 p v q -2 q -> t -3 ¬ t I- p
33 REGLAS DERIVADAS	-1 ¬r v ¬q -2 t v s -> r -3 q v ¬s -4 ¬t I- ¬(t v s)
34 REGLAS DERIVADAS	-1 p v q -2 t -> ¬p -3 ¬(q v r) I- ¬t
35 REGLAS DERIVADAS	-1 p -> ¬s -2 s v ¬r -3 ¬ (t v ¬r) I- ¬p
36 REGLAS DERIVADAS	-1 p -> q v r -2 q -> ¬p -3 s -> ¬r I- p -> ¬s
37 IC	-1 p v ¬s -2 ¬r -> s I- ¬p -> r
38 IC	-1 ¬(r & s) -2 q -> s I- r -> ¬q
39 IC	-1 s -> r -2 s v p -3 p -> q -4 r -> t I- ¬q -> t
40 IC	-1 ¬s <-> t & p -2 r -> ¬ s I- r-> t
41 IC	-1 s & (¬p v t) -2 t -> q v r I- p -> (¬q -> r)
42 IC	-1 p -> q -2 q -> r -3 r -> s v t I- ¬s & ¬t -> ¬p
43 IC	-1 p v q -> (r v s -> t) I- p -> (r -> t)
44 IC	-1 ¬ q -> ¬p -2 p -> (q -> r) -3 ¬(r -> s) -> ¬q I- p -> s
45 IC (146)	­1  ¬s v ¬p -2  q -> ¬r -3  t -> s & r I- t -> ¬(p v q)
46 IC (136)	- 1 (r v q) -> p - 2 t -> (¬p&¬m) - 3 t v s I- r -> s
47 IN	-1 ¬ (p & q) -2 ¬r -> ¬p -3 ¬q -> ¬r I- ¬p
48 IN	-1 t -> ¬s -2 r -> ¬t -3 s v r I- ¬t
49 IN	-1 ¬(p & q) -2 ¬ q -> r -3 ¬r -> p I- r
50 IN	-1 ¬(q v r) -2 t <-> ¬p -3 p v q I- ¬t
51 IN	-1 s -> ¬p -2 s v ¬r -3 ¬(t v¬r) I- ¬p
52 IN	-1 p -> q v r -2 q -> ¬p -3 s -> ¬r I- ¬ (p & s)
53 IN	-1 ¬r -> ¬s -2 t & r <-> ¬s I- r
54 IN	-1 ¬r v ¬q -2 t v s -> r -3 q v ¬s -4 ¬t I- ¬(t v s)
55 IN (152)	-1  (p v q) -> (r & s) -2  ¬r I- ¬ p
56 IN	-1 s -> p -2 r v ¬ p -3 t -> ¬r I- ¬s v ¬t
57 IN	-1 p -> ¬ q -2 r -> q I- ¬(p & q)
58 IN	-1 ( ¬q -> ¬p) & (¬p -> q) I- q
59 IN	-1 ¬(¬p & ¬r) -2 ¬s -> ¬r -3 p -> q I- q v s
60 IN	-1 ¬p -> s v r -2 ¬p & r -3 s -> q I- q v r
61 REGLAS DERIVADAS	-1 p v ¬(¬q & ¬r) -2 ¬p & ¬q I- r v s
62 IC	-1 ¬p -> q -2 q -> ¬r I- r -> p
63 IN	-1 p -> q -2 ¬(p & r) & (r v ¬q) I- ¬p
	Ejercicios de cálculo proposicional tomados de Montaner Pedro y Arnau Hilari: Teoría y práctica de la lógica proposicional, Vicens-Vives
64	- 1 s -> r - 2 s v p - 3 p -> q - 4 r -> t I- ¬ q -> t
65	- 1 t -> ¬s - 2 q -> ¬t - 3 s v q I- ¬t
66	- 1 (m&n)-> ¬t - 2 t v¬s - 3 ¬ (p v ¬s) I- ¬(m & n)
67	- 1 ¬ q v s - 2 ¬s - 3 ¬(r & s) -> q I- r
68	- 1 p v¬r - 2 ¬r -> s - 3 p -> t - 4 ¬s I- t
69	- 1 p-> ¬(s v ¬r) - 2 q -> ¬(m v r) - 3 ¬(¬u & ¬p) - 4 ¬(¬u & ¬q) I- u
70	- 1 p -> q - 2 (p->r) -> (svq) - 3 (p & q) -> r - 4 ¬s I- q
71	- 1 p -> ¬r - 2 q -> ¬s - 3 m -> (r & s) - 4 n -> (r & s) - 5 t -> ¬¬m - 6 ¬t -> ¬¬n I- ¬p v ¬q
72	- 1 (t & r) <-> s - 2 ¬r -> ¬s I- r
73	- 1 (p v q) -> r - 2 w-> ¬(m&s) - 3 ¬(tvn) ->m - 4 q <-> t v n - 5 s I- w -> r
74	- 1(p->q) & (r -> s) - 2 ¬q v ¬s - 3 ¬(p & r)->t I- t
75	- 1 ¬(¬q v ¬t) - 2 p -> m - 3 n -> ¬q - 4 p v n I- m
76	- 1¬p -> q - 2 ¬m -> n - 3 ¬r -> s - 4 ¬s -> x - 5 ¬(¬¬p v ¬¬m) - 6¬(¬¬r v ¬¬s) - 7 ¬(s -> ¬q) -> w - 8 ¬(n -> ¬x)-> u I- ¬(¬w v ¬u)
77	- 1 ¬(pvq) ->r - 2 ¬(w v m) - 3 ¬(z v n) - 4 ¬(mvn) ->t - 5 ¬(svp) - 6 ¬(u vq) I-¬(¬r v¬t)
78	- 1 p -> w - 2 q v ¬ w - 3 ¬( p & q) I- ¬ p
79	- 1 ¬(p & q) - 2 ¬r -> q - 3 ¬p -> r I- r
80	- 1 p -> q - 2 ¬ q - 3 ¬ p -> ( r & s) I- r & s
81	- 1 p & q - 2 r -> ¬q - 3 ¬r -> s I- s v¬p
82	- 1 r v s - 2 ¬t -> ¬p - 3 r -> ¬q I- (p & q) -> (s & t)
83	- 1 q -> p - 2 t v s - 3 q v ¬s I- ¬(p v r) -> t
84	- 1 p -> q - 2 (p & q) -> r - 3 ¬(p & r) I- ¬p
85	- 1 r -> ¬p - 2 ¬ (q & ¬r) I- p -> ¬q
86	- 1(s & ¬r) -> q - 2(¬t & ¬q) -> w - 3 t -> ¬m - 4 s - 5 ¬p v ¬q - 6 ¬(¬m & r) I- p -> w
87	- 1 ¬m v p - 2 q -> m - 3 x v t - 4 t -> (r & s) - 5 ( s & r )->w I-(¬p->¬q)->(¬w->x)
88	- 1 (p&q)->¬r - 2 r v (s&t) - 3 p <-> q I- p -> s
89	- 1 p->¬(¬rv¬s) - 2 ¬¬s ->¬u - 3 ¬m v n - 4¬n - 5 p & q I-¬(u v m)
90	- 1 t -> m - 2 ¬(u & p) - 3 n ->¬m - 4¬(¬p & ¬w) - 5 ¬n -> ¬s - 6 z -> u - 7 ¬(r v ¬t) - 8 ¬z -> s I- w v q
91	- 1 ¬p -> ¬ s - 2 ¬p v r - 3 r -> ¬t I- ¬s v ¬t
92	- 1 ¬t v ¬r - 2 ¬r -> p - 3 ¬(¬r &p) I- ¬t
93	- 1 r -> s - 2 s -> q - 3 r v (s & t) I- ¬q -> (t &s)
94	- 1 ¬r -> s - 2 s -> (p &q) - 3 r -> t - 4 ¬t I- q
95	- 1 ¬s v ¬r - 2 ¬r -> ¬t - 3 ¬p I- ¬t & ¬p
96	- 1 (r v q) -> p - 2 t -> (¬p&¬m) - 3 t v s I- r -> s
97	- 1 r -> n - 2 t -> (p v r) - 3 (q v n) -> t - 4 ¬n I- ¬p -> ¬q
98	- 1 ¬q -> ¬(mvt) - 2 ¬r -> ¬(p&q) - 3 ¬s -> p - 4 ¬n-> t I- ¬(r v s) -> n
99	- 1 p -> q - 2 p->(q -> r) - 3 q->( r -> s) I- p -> s
100	- 1 ¬p -> ¬s - 2¬p v r - 3 r -> ¬t I- ¬s v ¬t
101	- 1 ¬(m v n) - 2 s -> ¬t - 3 ¬m -> t I- ¬(s & q)
102	- 1 p->(q<->s) - 2 ¬s & m - 3 p v ¬q - 4 q & t I-(¬p &t) v (w & r)
	Más ejercicios de cálculo proposicional
103	- 1¬(m & ¬n) - 2¬(t & ¬u) - 3 ¬(n &¬p) - 4 ¬(s & ¬t) - 5¬(q & ¬r) - 6¬ (u v w) - 7 ¬(r &¬s) - 8 ¬(p &¬q) I- ¬m
104	- 1 s -> r - 2 s v p - 3 p -> q - 4 r -> t I- ¬ q -> t
105	- 1 t -> ¬s - 2 q -> ¬t - 3 s v q I- ¬t
106	- 1 (m&n)-> ¬t - 2 t v¬s - 3 ¬ (p v ¬s) I- ¬(m & n)
107	- 1 ¬ q v s - 2 ¬s - 3 ¬(r & s) -> q I- r
108	- 1 p v¬r - 2 ¬r -> s - 3 p -> t - 4 ¬s I- t
109	- 1 p-> ¬(s v ¬r) - 2 q -> ¬(m v r) - 3 ¬(¬u & ¬p) - 4 ¬(¬u & ¬q) I- u
110	- 1 p -> q - 2 (p->r) -> (svq) - 3 (p & q) -> r - 4 ¬s I- q
111	- 1 p -> ¬r - 2 q -> ¬s - 3 m -> (r & s) - 4 n -> (r & s) - 5 t -> ¬¬m - 6 ¬t -> ¬¬n I- ¬p v ¬q
112	- 1 (t & r) <-> s - 2 ¬r -> ¬s I- r
113	- 1 (p v q) -> r - 2 w-> ¬(m&s) - 3 ¬(tvn) ->m - 4 q <-> t v n - 5 s I- w -> r
114	- 1(p->q) & (r -> s) - 2 ¬q v ¬s - 3 ¬(p & r)->t I- t
115	- 1 ¬(¬q v ¬t) - 2 p -> m - 3 n -> ¬q - 4 p v n I- m
116	- 1¬p -> q - 2 ¬m -> n - 3 ¬r -> s - 4 ¬s -> x - 5 ¬(¬¬p v ¬¬m) - 6¬(¬¬r v ¬¬s) - 7 ¬(s -> ¬q) -> w - 8¬(n -> ¬x)-> u I- ¬(¬w v ¬u)
117	- 1 ¬(pvq) ->r - 2 ¬(w v m) - 3 ¬(z v n) - 4 ¬(mvn) ->t - 5 ¬(svp) - 6 ¬(u vq) I-¬(¬r v¬t)
118	- 1 p -> w - 2 q v ¬ w - 3 ¬( p & q) I- ¬ p
119	- 1 ¬(p & q) - 2 ¬r -> q - 3 ¬p -> r I- r
120	- 1 p -> q - 2 ¬ q - 3 ¬ p -> ( r & s) I- r & s
121	- 1 p & q - 2 r -> ¬q - 3 ¬r -> s I- s v¬p
122	- 1 r v s - 2 ¬t -> ¬p - 3 r -> ¬q I- (p & q) -> (s & t)
123	- 1 q -> p - 2 t v s - 3 q v ¬s I- ¬(p v r) -> t
124	- 1 p -> q - 2 (p & q) -> r - 3 ¬(p & r) I- ¬p
125	- 1 r -> ¬p - 2 ¬ (q & ¬r) I- p -> ¬q
126	- 1(s & ¬r) -> q - 2(¬t & ¬q) -> w - 3 t -> ¬m - 4 s - 5 ¬p v ¬q - 6 ¬(¬m & r) I- p -> w
127	- 1 ¬m v p - 2 q -> m - 3 x v t - 4 t -> (r & s) - 5 ( s & r )->w I-(¬p->¬q)->(¬w->x)
128	- 1 (p&q)->¬r - 2 r v (s&t) - 3 p <-> q I- p -> s
129	- 1 p->¬(¬rv¬s) - 2 ¬¬s ->¬u - 3 ¬m v n - 4¬n - 5 p & q I-¬(u v m)
130	- 1 t -> m - 2 ¬(u & p) - 3 n ->¬m - 4¬(¬p & ¬w) - 5 ¬n -> ¬s - 6 z -> u - 7 ¬(r v ¬t) - 8 ¬z -> s I- w v q
131	- 1 ¬p -> ¬ s - 2 ¬p v r - 3 r -> ¬t I- ¬s v ¬t
132	- 1 ¬t v ¬r - 2 ¬r -> p - 3 ¬(¬r &p) I- ¬t
133	- 1 r -> s - 2 s -> q - 3 r v (s & t) I- ¬q -> (t &s)
134	- 1 ¬r -> s - 2 s -> (p &q) - 3 r -> t - 4 ¬t I- q
135	- 1 ¬s v ¬r - 2 ¬r -> ¬t - 3 ¬p I- ¬t & ¬p
136	- 1 (r v q) -> p - 2 t -> (¬p&¬m) - 3 t v s I- r -> s
137	- 1 r -> n - 2 t -> (p v r) - 3 (q v n) -> t - 4 ¬n I- ¬p -> ¬q
138	- 1 ¬q -> ¬(mvt) - 2 ¬r -> ¬(p&q) - 3 ¬s -> p - 4 ¬n-> t I- ¬(r v s) -> n
139	- 1 p -> q - 2 p->(q -> r) - 3 q->( r -> s) I- p -> s
140	- 1 ¬p -> ¬s - 2¬p v r - 3 r -> ¬t I- ¬s v ¬t
141	- 1 ¬(m v n) - 2 s -> ¬t - 3 ¬m -> t I- ¬(s & q)
142	- 1 p->(q<->s) - 2 ¬s & m - 3 p v ¬q - 4 q & t I-(¬p &t)v(w & r)
143	- 1¬(m & ¬n) - 2¬(t & ¬u) - 3 ¬(n &¬p) - 4 ¬(s & ¬t) - 5¬(q & ¬r) - 6¬ (u v w) - 7 ¬(r &¬s) - 8 ¬(p &¬q) I- ¬m
144	-1 ¬q -> r -2 t -> ¬ q -3 ¬ s -> ¬ q I- t v ¬s -> r
145	1. – ¬(p & q) 2. – p -> r 3. – q v ¬r I- ¬p
146	1. ­ ¬s v ¬p 2. – q -> ¬r 3. – t -> s & r I- t -> ¬(p v q)
147	1. – p &¬q 2. – ¬r -> q 3. – r -> s I- p & s
148	1. – p & ¬t 2. – s -> t 3. ­ s v q 4. – (q v p)-> u I- u
149	1. – ¬r -> s 2. – s -> (p & q) 3. – r -> (t & w) 4. – ¬ t I- q v (m & n)
150	1.-m->¬ (¬p&¬q) 2. – q -> t 3. – p -> s I- m -> ¬(¬t & ¬s)
151	1. – p & ¬q 2. – q v ¬r 3. – p -> ¬s I- ¬(s v r)
152	1. – (p v q) -> (r&s) 2. – ¬r I- ¬p
153	1. – p -> q 2. – q v r 3.- (r&¬p)->(s&¬p) 4.- ¬q I- s
154	1.- ¬s->¬(p v ¬t) 2.- t->¬(¬w v ¬n) 3. – ¬s & ¬w I- m v n
155	1. – ¬(¬mv¬s) 2. – u -> q 3. – t -> ¬q 4. – w -> t 5. – ¬m v w I- ¬(u & n)
156	1. – p -> q 2. – t -> m 3. – ¬(u &w) 4. – ¬(¬p v ¬z) 5. – ¬r -> ¬q 6. – n -> u 7. – ¬t -> s 8. -¬(m & ¬n) 9. – r -> ¬s I-¬w