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Lógica matemática/ abc∨¬adc∨¬a¬bc∨¬ab¬c∨¬a¬b¬c

Expresión abc∨¬adc∨¬a¬bc∨¬ab¬c∨¬a¬b¬c

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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