Expresión dc∨bd⇒(db⇔dc)∨db⇒c

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Solución

Ha introducido [src]

(((b∧d)∨(c∧d))⇒((b∧d)∨((b∧d)⇔(c∧d))))⇒c

$$\left(\left(\left(b \wedge d\right) \vee \left(c \wedge d\right)\right) \Rightarrow \left(\left(b \wedge d\right) \vee \left(\left(b \wedge d\right) ⇔ \left(c \wedge d\right)\right)\right)\right) \Rightarrow c$$

Solución detallada

$$\left(b \wedge d\right) \vee \left(c \wedge d\right) = d \wedge \left(b \vee c\right)$$
$$\left(b \wedge d\right) ⇔ \left(c \wedge d\right) = \left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right) \vee \neg d$$
$$\left(b \wedge d\right) \vee \left(\left(b \wedge d\right) ⇔ \left(c \wedge d\right)\right) = b \vee \neg c \vee \neg d$$
$$\left(\left(b \wedge d\right) \vee \left(c \wedge d\right)\right) \Rightarrow \left(\left(b \wedge d\right) \vee \left(\left(b \wedge d\right) ⇔ \left(c \wedge d\right)\right)\right) = b \vee \neg c \vee \neg d$$
$$\left(\left(\left(b \wedge d\right) \vee \left(c \wedge d\right)\right) \Rightarrow \left(\left(b \wedge d\right) \vee \left(\left(b \wedge d\right) ⇔ \left(c \wedge d\right)\right)\right)\right) \Rightarrow c = c$$

Simplificación [src]

$$c$$

Tabla de verdad

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

FNDP [src]

$$c$$

FND [src]

Ya está reducido a FND

$$c$$

FNCD [src]

$$c$$

FNC [src]

Ya está reducido a FNC

$$c$$

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Expresión dc∨bd⇒(db⇔dc)∨db⇒c

Solución