Sr Examen
Expresión CA+¬B↔BC→¬A¬BA→C
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬b)∨(a∧c))⇔(((b∧c)⇒(a∧(¬a)∧(¬b)))⇒c)
$$\left(\left(\left(b \wedge c\right) \Rightarrow \left(a \wedge \neg a \wedge \neg b\right)\right) \Rightarrow c\right) ⇔ \left(\left(a \wedge c\right) \vee \neg b\right)$$
Solución detallada
$$a \wedge \neg a \wedge \neg b = \text{False}$$
$$\left(b \wedge c\right) \Rightarrow \left(a \wedge \neg a \wedge \neg b\right) = \neg b \vee \neg c$$
$$\left(\left(b \wedge c\right) \Rightarrow \left(a \wedge \neg a \wedge \neg b\right)\right) \Rightarrow c = c$$
$$\left(\left(\left(b \wedge c\right) \Rightarrow \left(a \wedge \neg a \wedge \neg b\right)\right) \Rightarrow c\right) ⇔ \left(\left(a \wedge c\right) \vee \neg b\right) = \left(a \wedge b\right) \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
$$\left(b \wedge c\right) \Rightarrow \left(a \wedge \neg a \wedge \neg b\right) = \neg b \vee \neg c$$
$$\left(\left(b \wedge c\right) \Rightarrow \left(a \wedge \neg a \wedge \neg b\right)\right) \Rightarrow c = c$$
$$\left(\left(\left(b \wedge c\right) \Rightarrow \left(a \wedge \neg a \wedge \neg b\right)\right) \Rightarrow c\right) ⇔ \left(\left(a \wedge c\right) \vee \neg b\right) = \left(a \wedge b\right) \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
Simplificación
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$$\left(a \wedge b\right) \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
(a∧b)∨(b∧(¬c))∨(c∧(¬b))
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNCD
[src]
$$\left(b \vee c\right) \wedge \left(a \vee \neg b \vee \neg c\right)$$
(b∨c)∧(a∨(¬b)∨(¬c))
FND
[src]
Ya está reducido a FND
$$\left(a \wedge b\right) \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
(a∧b)∨(b∧(¬c))∨(c∧(¬b))
FNDP
[src]
$$\left(a \wedge b\right) \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
(a∧b)∨(b∧(¬c))∨(c∧(¬b))
FNC
[src]
$$\left(b \vee c\right) \wedge \left(b \vee \neg b\right) \wedge \left(a \vee b \vee c\right) \wedge \left(a \vee b \vee \neg b\right) \wedge \left(a \vee c \vee \neg c\right) \wedge \left(a \vee \neg b \vee \neg c\right) \wedge \left(b \vee c \vee \neg c\right) \wedge \left(b \vee \neg b \vee \neg c\right)$$
(b∨c)∧(b∨(¬b))∧(a∨b∨c)∧(a∨b∨(¬b))∧(a∨c∨(¬c))∧(b∨c∨(¬c))∧(a∨(¬b)∨(¬c))∧(b∨(¬b)∨(¬c))