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