Sr Examen
Lógica matemática/ ¬(¬a∧(b∨c∨d))

Expresión ¬(¬a∧(b∨c∨d))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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