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