Sr Examen
Expresión (bvcvd)⇒d(avb)va(b⇔d)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(b∨c∨d)⇒((a∧(b⇔d))∨(d∧(a∨b)))
$$\left(b \vee c \vee d\right) \Rightarrow \left(\left(a \wedge \left(b ⇔ d\right)\right) \vee \left(d \wedge \left(a \vee b\right)\right)\right)$$
Solución detallada
$$b ⇔ d = \left(b \wedge d\right) \vee \left(\neg b \wedge \neg d\right)$$
$$a \wedge \left(b ⇔ d\right) = a \wedge \left(b \vee \neg d\right) \wedge \left(d \vee \neg b\right)$$
$$\left(a \wedge \left(b ⇔ d\right)\right) \vee \left(d \wedge \left(a \vee b\right)\right) = \left(a \wedge \neg b\right) \vee \left(b \wedge d\right)$$
$$\left(b \vee c \vee d\right) \Rightarrow \left(\left(a \wedge \left(b ⇔ d\right)\right) \vee \left(d \wedge \left(a \vee b\right)\right)\right) = \left(a \wedge \neg b\right) \vee \left(b \wedge d\right) \vee \left(\neg b \wedge \neg c \wedge \neg d\right)$$
$$a \wedge \left(b ⇔ d\right) = a \wedge \left(b \vee \neg d\right) \wedge \left(d \vee \neg b\right)$$
$$\left(a \wedge \left(b ⇔ d\right)\right) \vee \left(d \wedge \left(a \vee b\right)\right) = \left(a \wedge \neg b\right) \vee \left(b \wedge d\right)$$
$$\left(b \vee c \vee d\right) \Rightarrow \left(\left(a \wedge \left(b ⇔ d\right)\right) \vee \left(d \wedge \left(a \vee b\right)\right)\right) = \left(a \wedge \neg b\right) \vee \left(b \wedge d\right) \vee \left(\neg b \wedge \neg c \wedge \neg d\right)$$
Simplificación
[src]
$$\left(a \wedge \neg b\right) \vee \left(b \wedge d\right) \vee \left(\neg b \wedge \neg c \wedge \neg d\right)$$
(b∧d)∨(a∧(¬b))∨((¬b)∧(¬c)∧(¬d))
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+
FNDP
[src]
$$\left(a \wedge \neg b\right) \vee \left(b \wedge d\right) \vee \left(\neg b \wedge \neg c \wedge \neg d\right)$$
(b∧d)∨(a∧(¬b))∨((¬b)∧(¬c)∧(¬d))
FND
[src]
Ya está reducido a FND
$$\left(a \wedge \neg b\right) \vee \left(b \wedge d\right) \vee \left(\neg b \wedge \neg c \wedge \neg d\right)$$
(b∧d)∨(a∧(¬b))∨((¬b)∧(¬c)∧(¬d))
FNCD
[src]
$$\left(d \vee \neg b\right) \wedge \left(a \vee b \vee \neg d\right) \wedge \left(a \vee d \vee \neg c\right)$$
(d∨(¬b))∧(a∨b∨(¬d))∧(a∨d∨(¬c))
FNC
[src]
$$\left(b \vee \neg b\right) \wedge \left(d \vee \neg b\right) \wedge \left(a \vee b \vee \neg b\right) \wedge \left(a \vee b \vee \neg c\right) \wedge \left(a \vee b \vee \neg d\right) \wedge \left(a \vee d \vee \neg b\right) \wedge \left(a \vee d \vee \neg c\right) \wedge \left(a \vee d \vee \neg d\right) \wedge \left(b \vee \neg b \vee \neg c\right) \wedge \left(b \vee \neg b \vee \neg d\right) \wedge \left(d \vee \neg b \vee \neg c\right) \wedge \left(d \vee \neg b \vee \neg d\right)$$
(b∨(¬b))∧(d∨(¬b))∧(a∨b∨(¬b))∧(a∨b∨(¬c))∧(a∨b∨(¬d))∧(a∨d∨(¬b))∧(a∨d∨(¬c))∧(a∨d∨(¬d))∧(b∨(¬b)∨(¬c))∧(b∨(¬b)∨(¬d))∧(d∨(¬b)∨(¬c))∧(d∨(¬b)∨(¬d))