logic exercises
week / propositional logic
"If
"
Ta the Sun shines today ,
then it won't shine tomor row .
p sun shines today
& Sun shines tomorrow
a
-
p
-
b "Robert was jealous of yuonne , or he was not in a good mood .
"
p robert wa s jealous of yronne
& rober t is in a good mood
pv =
C "if the barometer falls ,
then either it will rain or it will snow .
"
p the barometer falls
9 it rains
r it snows
p +
(avr) = p +
(q0r) =
p
+
((av ur)v( -
q1 r)
& "alzheimer's disease will not be cured unless its cause is determined and a new
"
found
drug for it is .
p alzheimer's disease is cured
9 cause of alzheimer's is determined
found
~ a new drug is
(91 r =
v(q -
r)
-
p +
p -
e no shoes
,
no shirt ,
no service.
p shoes
a shirt
r service
-p1
-
a - - = -up + +
9)v + r = pvq v -p
2 reinsert parentheses
a -
p1q + r
( -
(p) -a) - r
D(p +
q)1 -
(rvp -
a)
(p -
a)1( -
() r vp) >
-
a)
c
pv / - a -
p1 r
pv(
-
(q) -(p - r)
,& p V a
1 r is problematic because we do not know if it is supposed to be
(pra)1r or pv(q + r) .
3 omit parentheses
a( (p
-
(91 r)) -
( (p)v (r)))
-
- -
(p1q1r)
-
+ -
pv
-
r
D( -
(p 1(qvr)) - -
(p))v -
(r)
↑ (p +
(avr)) - -
p)v -
r
4 parse trees
a -
((va -
(p =
r)) +(r +
a)
-
( -
q1(p = rs)1(r -
q)
G
& asper crea
u
au(p r
-
- -
a
. por
⑮
⑨
↓
p(p -
a) -
( -
rv(q -
r)
(p1q) + ( +
r
v(q + r)
·
⑤
Greger
v ②
a er
i
A formula which is a
disjunction whose disjunctions a re conjunctions .
↳ (0 , 102)v(4 -
-
+)
6 15 ( (p s))))
(av
- -
- + -
①
↓ s - (v(p +
(av - s))
②
⑤ ↳ -specars)
& pe saves
& av- s
d
⑤
, (u/pv(91 (p))
- +
-
7
-
(pv(q1 -
p)) = r
-
(pv(q1 -
p)
pv(q1 -
p)
91 +
p
7 p
Ba false
P T
-
= F
& true
F + F =
T
-> T = F
r false
F
F VT =
T
T1T = T
F
- F = T
T
F
-F = T
D false
p
TF
false F
=
9
p false - F = T
FVF
F
= F
F1T = F
F -F = T
F
F
ga((pe -
q)e -
p) -
q
& ↑ XS
P 9
-
a P -> -
9 -
P P -
-p 4 -
9 p a
-
p
- -
9 Xvg
1 g 1 1 I
1 g g 1 I
↑ O 1 I
O g 1 O 1 1
G 1 O I I 1 1 I 1
1
g O 1 1 I I g 1 1 1
↳
contingent
n(p -
q)v(p + -
a)
↳ tautology
, ?
10p -
(9vr) =
11
up"
IS
"-prq vr" -
9 vr "-PV r va
P & r P 9 r
p
+
jqv rS av) pvr) 91 r -
p1 =r -
d
- - -
p
- -
T 11 o o O 1 1 1 I
1 10 O O f 1 ↑ 1 I
1 o 10 I O 1 I I 1
1 O 00 I I O O 1 O
O 1 1100 1 I 1 1
G 1 o 10 1 1 1 I
O
001 1 I G 1 I I I
000 1. I I 1 - I
p
>
-
(qvr) =
qV( prr)
-
11 associative
p
+
q = r =
(p =
q) = =
p
=
(q =
r) ?
& ↓
pa j
pa ① p
9 r p + 4
1 1 I 1 1 1 1
1 1 1 O G O
O
1 O 1 O oo O
1 C o o 11 1
& 1 10 0 1 0
O 1 o o 1 . 1
o O I f 1 o
00 0 g 1 O
1
PSciative
week / propositional logic
"If
"
Ta the Sun shines today ,
then it won't shine tomor row .
p sun shines today
& Sun shines tomorrow
a
-
p
-
b "Robert was jealous of yuonne , or he was not in a good mood .
"
p robert wa s jealous of yronne
& rober t is in a good mood
pv =
C "if the barometer falls ,
then either it will rain or it will snow .
"
p the barometer falls
9 it rains
r it snows
p +
(avr) = p +
(q0r) =
p
+
((av ur)v( -
q1 r)
& "alzheimer's disease will not be cured unless its cause is determined and a new
"
found
drug for it is .
p alzheimer's disease is cured
9 cause of alzheimer's is determined
found
~ a new drug is
(91 r =
v(q -
r)
-
p +
p -
e no shoes
,
no shirt ,
no service.
p shoes
a shirt
r service
-p1
-
a - - = -up + +
9)v + r = pvq v -p
2 reinsert parentheses
a -
p1q + r
( -
(p) -a) - r
D(p +
q)1 -
(rvp -
a)
(p -
a)1( -
() r vp) >
-
a)
c
pv / - a -
p1 r
pv(
-
(q) -(p - r)
,& p V a
1 r is problematic because we do not know if it is supposed to be
(pra)1r or pv(q + r) .
3 omit parentheses
a( (p
-
(91 r)) -
( (p)v (r)))
-
- -
(p1q1r)
-
+ -
pv
-
r
D( -
(p 1(qvr)) - -
(p))v -
(r)
↑ (p +
(avr)) - -
p)v -
r
4 parse trees
a -
((va -
(p =
r)) +(r +
a)
-
( -
q1(p = rs)1(r -
q)
G
& asper crea
u
au(p r
-
- -
a
. por
⑮
⑨
↓
p(p -
a) -
( -
rv(q -
r)
(p1q) + ( +
r
v(q + r)
·
⑤
Greger
v ②
a er
i
A formula which is a
disjunction whose disjunctions a re conjunctions .
↳ (0 , 102)v(4 -
-
+)
6 15 ( (p s))))
(av
- -
- + -
①
↓ s - (v(p +
(av - s))
②
⑤ ↳ -specars)
& pe saves
& av- s
d
⑤
, (u/pv(91 (p))
- +
-
7
-
(pv(q1 -
p)) = r
-
(pv(q1 -
p)
pv(q1 -
p)
91 +
p
7 p
Ba false
P T
-
= F
& true
F + F =
T
-> T = F
r false
F
F VT =
T
T1T = T
F
- F = T
T
F
-F = T
D false
p
TF
false F
=
9
p false - F = T
FVF
F
= F
F1T = F
F -F = T
F
F
ga((pe -
q)e -
p) -
q
& ↑ XS
P 9
-
a P -> -
9 -
P P -
-p 4 -
9 p a
-
p
- -
9 Xvg
1 g 1 1 I
1 g g 1 I
↑ O 1 I
O g 1 O 1 1
G 1 O I I 1 1 I 1
1
g O 1 1 I I g 1 1 1
↳
contingent
n(p -
q)v(p + -
a)
↳ tautology
, ?
10p -
(9vr) =
11
up"
IS
"-prq vr" -
9 vr "-PV r va
P & r P 9 r
p
+
jqv rS av) pvr) 91 r -
p1 =r -
d
- - -
p
- -
T 11 o o O 1 1 1 I
1 10 O O f 1 ↑ 1 I
1 o 10 I O 1 I I 1
1 O 00 I I O O 1 O
O 1 1100 1 I 1 1
G 1 o 10 1 1 1 I
O
001 1 I G 1 I I I
000 1. I I 1 - I
p
>
-
(qvr) =
qV( prr)
-
11 associative
p
+
q = r =
(p =
q) = =
p
=
(q =
r) ?
& ↓
pa j
pa ① p
9 r p + 4
1 1 I 1 1 1 1
1 1 1 O G O
O
1 O 1 O oo O
1 C o o 11 1
& 1 10 0 1 0
O 1 o o 1 . 1
o O I f 1 o
00 0 g 1 O
1
PSciative
