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Lógica matemática/ A⇒B⇒(B⇒C⇒(A∨B⇒C))

Expresión A⇒B⇒(B⇒C⇒(A∨B⇒C))

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    Solución

    Ha introducido [src] 
    (a⇒b)⇒((b⇒c)⇒((a∨b)⇒c))
    (a⇒b)⇒((b⇒c)⇒((a∨b)⇒c))\left(a \Rightarrow b\right) \Rightarrow \left(\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right)\right)
    Solución detallada
    a⇒b=b∨¬aa \Rightarrow b = b \vee \neg a
    b⇒c=c∨¬bb \Rightarrow c = c \vee \neg b
    (a∨b)⇒c=c∨(¬a∧¬b)\left(a \vee b\right) \Rightarrow c = c \vee \left(\neg a \wedge \neg b\right)
    (b⇒c)⇒((a∨b)⇒c)=b∨c∨¬a\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right) = b \vee c \vee \neg a
    (a⇒b)⇒((b⇒c)⇒((a∨b)⇒c))=1\left(a \Rightarrow b\right) \Rightarrow \left(\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right)\right) = 1
    Simplificación [src]
    1 
    1
    Tabla de verdad 
    +---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 1      |
+---+---+---+--------+
| 0 | 0 | 1 | 1      |
+---+---+---+--------+
| 0 | 1 | 0 | 1      |
+---+---+---+--------+
| 0 | 1 | 1 | 1      |
+---+---+---+--------+
| 1 | 0 | 0 | 1      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FNDP [src]
    1 
    1
    FNC [src]
    Ya está reducido a FNC
    1 
    1
    FNCD [src]
    1 
    1
    FND [src]
    Ya está reducido a FND
    1 
    1
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