jueves, 10 de marzo de 2011

TAREA II

1     
p
q
p ʌ q
1
1
1
1
0
0
0
1
0
0
0
0





    


2
p
q
r
(p ʌ q)
(p ʌ q) ʌ r
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0





3
p
q
¬q
(p → ¬q)
(p ʌ ¬q)
¬(p → ¬q)
¬(p → ¬q) ʌ (p ʌ ¬q)
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0





4
p
q
(p ʌ q)
¬q
(p v ¬q)
(p ʌ q) v (p v ¬q)
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1





5
p
q
r
(p ʌ q)
(p ʌ q) ʌ r
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0




6
p
q
¬q
(p ʌ ¬q)
¬(p ʌ ¬q)
¬(p ʌ ¬q) ʌ (p ʌ ¬q)
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0




7
p
q
¬p
¬q
(¬p ʌ ¬q)
(p ʌ ¬q)
(¬p ʌ ¬q) v (p ʌ ¬q)
¬(¬p ʌ ¬q) v (p ʌ ¬q)
¬¬(¬p ʌ ¬q) v (p ʌ ¬q)
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1



8
p
q
r
(p v q)
(p v q) ʌ r

1
1
1
1
1

1
1
0
1
0

1
0
1
1
1

1
0
0
1
0

0
1
1
1
1

0
1
0
1
0

0
0
1
0
0

0
0
0
0
0

9
p
q
¬p
¬q
(¬p ʌ ¬q)
¬(¬p ʌ ¬q)
¬(¬p ʌ ¬q) ʌ (¬p ʌ ¬q)
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0







10
p
q
r
¬r
(p v q)
(p v q) ʌ ¬r
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0





11
p
q
r
(p ʌ q)
(p ʌ q) → r
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1



12
p
q
r
¬r
(p ʌ q)
(p ʌ q) → ¬r
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1



13
p
¬p
p ↔ ¬p
1
0
0
0
1
0




14
p
q
¬q
(p ʌ ¬q)
¬(p ʌ ¬q)
¬(p ʌ ¬q) ʌ (p ʌ ¬q)
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0




15
p
q
¬p
¬q
¬¬p
¬¬q
¬¬p v ¬¬q
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0



16
p
q
p v q

1
1
1

1
0
1

0
1
0

0
0
1

17
p
q
r
(p ↔ q)
(p ↔ q) v r
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1





18
p
q
¬p
(¬p v q)
(p ʌ q)
(¬p v q) v (p ʌ q)
(¬p v q) v ¬p
[(¬p v q) v (p ʌ q)] → [(¬p v q) v ¬p]
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1





19
p
q
¬q
(p v ¬q)
¬p
(¬p → ¬q)
(p v ¬q) → (¬p → ¬q)
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1





20
p
q
¬q
(p ↔ ¬q)
(p v ¬q)
(p ↔ ¬q) v (p v ¬q)
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1




21
p
q
¬p
(¬p ʌ q)
(¬p → q)
(¬p ʌ q) v (¬p → q)
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0





22
p
q
¬q
¬p
¬q v ¬p
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1





23
p
q
r
p → q
(p → q) ʌ r
¬q
(¬q v r)
¬(¬q v r)
¬r
¬(¬q v r) v ¬r
[(p → q) ʌ r] ↔ [¬(¬q v r) v ¬r]
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0





24
q
r
¬q
(¬q ʌ r)
(¬q v r)
¬(¬q v r)
¬r
¬(¬q v r) v ¬r
(¬q ʌ r) → ¬(¬q v r) v ¬r
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1



25
p
q
r
(p → q)
(p → q) ʌ r
(p v r)
¬(p v r)
¬r
¬(p v r) v ¬r
(p → q) ʌ r → ¬(p v r) v ¬r
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1


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