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Lógica matemática/ (((¬A∨B)⇒C)∨(¬D⇒((B∧C)∨A)))

Expresión (((¬A∨B)⇒C)∨(¬D⇒((B∧C)∨A)))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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