Sr Examen
Expresión a(c-b)-b(c-a)+c(b-a)
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Solución
Ha introducido
[src]
(a∧(c|b))|((b∧(c|a))∨(c∧(b|a)))
$$\left(a \wedge \left(c | b\right)\right) | \left(\left(b \wedge \left(c | a\right)\right) \vee \left(c \wedge \left(b | a\right)\right)\right)$$
Solución detallada
$$c | b = \neg b \vee \neg c$$
$$a \wedge \left(c | b\right) = a \wedge \left(\neg b \vee \neg c\right)$$
$$c | a = \neg a \vee \neg c$$
$$b \wedge \left(c | a\right) = b \wedge \left(\neg a \vee \neg c\right)$$
$$b | a = \neg a \vee \neg b$$
$$c \wedge \left(b | a\right) = c \wedge \left(\neg a \vee \neg b\right)$$
$$\left(b \wedge \left(c | a\right)\right) \vee \left(c \wedge \left(b | a\right)\right) = \left(b \wedge \neg a\right) \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
$$\left(a \wedge \left(c | b\right)\right) | \left(\left(b \wedge \left(c | a\right)\right) \vee \left(c \wedge \left(b | a\right)\right)\right) = \left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right) \vee \neg a$$
$$a \wedge \left(c | b\right) = a \wedge \left(\neg b \vee \neg c\right)$$
$$c | a = \neg a \vee \neg c$$
$$b \wedge \left(c | a\right) = b \wedge \left(\neg a \vee \neg c\right)$$
$$b | a = \neg a \vee \neg b$$
$$c \wedge \left(b | a\right) = c \wedge \left(\neg a \vee \neg b\right)$$
$$\left(b \wedge \left(c | a\right)\right) \vee \left(c \wedge \left(b | a\right)\right) = \left(b \wedge \neg a\right) \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)$$
$$\left(a \wedge \left(c | b\right)\right) | \left(\left(b \wedge \left(c | a\right)\right) \vee \left(c \wedge \left(b | a\right)\right)\right) = \left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right) \vee \neg a$$
Simplificación
[src]
$$\left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right) \vee \neg a$$
(¬a)∨(b∧c)∨((¬b)∧(¬c))
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNC
[src]
$$\left(b \vee \neg a \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg a \vee \neg c\right)$$
(b∨(¬a)∨(¬b))∧(b∨(¬a)∨(¬c))∧(c∨(¬a)∨(¬b))∧(c∨(¬a)∨(¬c))
FND
[src]
Ya está reducido a FND
$$\left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right) \vee \neg a$$
(¬a)∨(b∧c)∨((¬b)∧(¬c))
FNCD
[src]
$$\left(b \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right)$$
(b∨(¬a)∨(¬c))∧(c∨(¬a)∨(¬b))
FNDP
[src]
$$\left(b \wedge c\right) \vee \left(\neg b \wedge \neg c\right) \vee \neg a$$
(¬a)∨(b∧c)∨((¬b)∧(¬c))