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

Expresión ¬(((A∨B)⇒C∧D)∧((D∨B)⇒F))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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