Sr Examen
Lógica matemática/ abc+a!b!c+acd+bcd+!a!bc!d

Expresión abc+a!b!c+acd+bcd+!a!bc!d

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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