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