Sr Examen
Lógica matemática/ AC´B´+AB´CD+A´B´D´+A´B´D´+A´B´C´

Expresión AC´B´+AB´CD+A´B´D´+A´B´D´+A´B´C´

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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