# Usuario:Galindo6/ejercicio 6

• ejercicios 1.1, pagina 13

## 25.

Construct a truth table for each of the following compound propositions.

a) ${\displaystyle p\to }$ (${\displaystyle \sim q}$${\displaystyle \lor r}$)

b) ${\displaystyle \sim p}$${\displaystyle \to }$(${\displaystyle q\to r}$)

c) (${\displaystyle p\to q}$)${\displaystyle \lor }$(${\displaystyle \sim p}$${\displaystyle \to r}$)

d) (${\displaystyle p\to q}$)${\displaystyle \land }$(${\displaystyle \sim p}$${\displaystyle \to r}$)

== SOLUCION == (respuestas en minuscula)

A) ${\displaystyle p\to }$ (${\displaystyle \sim q}$${\displaystyle \lor r}$)

V  v   F   v  V
V  f   F   f  F
V  v   V   v  V
V  v   V   v  F
F  v   F   v  V
F  v   F   f  F
F  v   V   v  V
F  v   V   v  F


B) ${\displaystyle \sim p}$${\displaystyle \to }$(${\displaystyle q\to r}$)

 F  v    V  v   V
F  v    V  f   F
F  v    F  v   V
F  v    F  v   F
V  v    V  v   V
V  f    V  f   F
V  v    F  v   V
V  v    F  v   F


C) (${\displaystyle p\to q}$)${\displaystyle \lor }$(${\displaystyle \sim p}$${\displaystyle \to r}$)

 V  v  V  v   F   v  V
V  v  V  v   F   v  F
V  f  F  v   F   v  V
V  f  V  v   F   v  F
F  v  V  v   V   v  V
F  v  V  v   V   f  F
F  v  V  v   V   v  V
F  v  V  v   V   f  F


D) (${\displaystyle p\to q}$)${\displaystyle \land }$(${\displaystyle \sim p}$${\displaystyle \to r}$)

 V  v  V  v   F   v  V
V  v  V  v   F   v  F
V  f  F  f   F   v  V
V  f  V  f   F   v  F
F  v  V  v   V   v  V
F  v  V  f   V   f  F
F  v  V  v   V   v  V
F  v  V  f   V   f  F


== pagina del solucionario == http://es.wikibooks.org/wiki/Pensamiento_Algor%C3%ADtmico:Solucionario