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

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución

Ha introducido [src]

(a∧(¬(c∨(¬(a∧(¬b))))))∨(¬((a∧(¬b))∨(c∧(¬a))))

$$\left(a \wedge \neg \left(c \vee \neg \left(a \wedge \neg b\right)\right)\right) \vee \neg \left(\left(a \wedge \neg b\right) \vee \left(c \wedge \neg a\right)\right)$$

Solución detallada

$$\neg \left(a \wedge \neg b\right) = b \vee \neg a$$
$$c \vee \neg \left(a \wedge \neg b\right) = b \vee c \vee \neg a$$
$$\neg \left(c \vee \neg \left(a \wedge \neg b\right)\right) = a \wedge \neg b \wedge \neg c$$
$$a \wedge \neg \left(c \vee \neg \left(a \wedge \neg b\right)\right) = a \wedge \neg b \wedge \neg c$$
$$\neg \left(\left(a \wedge \neg b\right) \vee \left(c \wedge \neg a\right)\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg c\right)$$
$$\left(a \wedge \neg \left(c \vee \neg \left(a \wedge \neg b\right)\right)\right) \vee \neg \left(\left(a \wedge \neg b\right) \vee \left(c \wedge \neg a\right)\right) = \left(a \wedge b\right) \vee \neg c$$

Simplificación [src]

$$\left(a \wedge b\right) \vee \neg c$$

(¬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 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+

FND [src]

Ya está reducido a FND

$$\left(a \wedge b\right) \vee \neg c$$

(¬c)∨(a∧b)

FNDP [src]

$$\left(a \wedge b\right) \vee \neg c$$

(¬c)∨(a∧b)

FNC [src]

$$\left(a \vee \neg c\right) \wedge \left(b \vee \neg c\right)$$

(a∨(¬c))∧(b∨(¬c))

FNCD [src]

$$\left(a \vee \neg c\right) \wedge \left(b \vee \neg c\right)$$

(a∨(¬c))∧(b∨(¬c))

¿Cómo usar?

Expresiones idénticas

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

Solución