# Usuario:Galindo6/ejercicio 5

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• ejercicios 1.1, pagina 13

## 23.

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

a) ${\displaystyle p\to }$${\displaystyle \sim q}$

b) ${\displaystyle \sim p}$${\displaystyle \leftrightarrow q}$

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

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

## SOLUCION

A) ${\displaystyle p\to }$${\displaystyle \sim q}$

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


B) ${\displaystyle \sim p}$${\displaystyle \leftrightarrow q}$

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


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

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


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

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


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