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Lógica matemática/ ((AvB)⇒C&D)&((DvB)⇒F)

Expresión ((AvB)⇒C&D)&((DvB)⇒F)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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