Sr Examen
Lógica matemática/ не(a)&B&C&DvA&не(B)&не(C)&DVA&B&не(C)&не(D)

Expresión не(a)&B&C&DvA&не(B)&не(C)&DVA&B&не(C)&не(D)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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