Sr Examen
Lógica matemática/ ((a&¬b)v(c&¬a))v(¬(¬(a&¬b)vc)&a)

Expresión ((a&¬b)v(c&¬a))v(¬(¬(a&¬b)vc)&a)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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