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Lógica matemática/ notbandnotdornotaand(dornotbcorbnotc)

Expresión notbandnotdornotaand(dornotbcorbnotc)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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