Sr Examen
Lógica matemática/ cva&b'va'&c'

Expresión cva&b'va'&c'

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    Solución

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