Expresión ¬(¬(a&b)v¬(cvb)&avc)v¬(bvc)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución

Ha introducido [src]

(¬(b∨c))∨(¬(c∨(¬(a∧b))∨(a∧(¬(b∨c)))))

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

Solución detallada

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

Simplificación [src]

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

(¬c)∧(a∨(¬b))

Tabla de verdad

+---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 1      |
+---+---+---+--------+
| 0 | 0 | 1 | 0      |
+---+---+---+--------+
| 0 | 1 | 0 | 0      |
+---+---+---+--------+
| 0 | 1 | 1 | 0      |
+---+---+---+--------+
| 1 | 0 | 0 | 1      |
+---+---+---+--------+
| 1 | 0 | 1 | 0      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 0      |
+---+---+---+--------+

FND [src]

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

(a∧(¬c))∨((¬b)∧(¬c))

FNC [src]

Ya está reducido a FNC

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

(¬c)∧(a∨(¬b))

FNDP [src]

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

(a∧(¬c))∨((¬b)∧(¬c))

FNCD [src]

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

(¬c)∧(a∨(¬b))

¿Cómo usar?

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Expresión ¬(¬(a&b)v¬(cvb)&avc)v¬(bvc)

Solución