Sr Examen
Expresión ¬(avb)v¬(cv¬a)v¬(¬bvc)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(a∨b))∨(¬(c∨(¬a)))∨(¬(c∨(¬b)))
$$\neg \left(a \vee b\right) \vee \neg \left(c \vee \neg a\right) \vee \neg \left(c \vee \neg b\right)$$
Solución detallada
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(c \vee \neg a\right) = a \wedge \neg c$$
$$\neg \left(c \vee \neg b\right) = b \wedge \neg c$$
$$\neg \left(a \vee b\right) \vee \neg \left(c \vee \neg a\right) \vee \neg \left(c \vee \neg b\right) = \left(\neg a \wedge \neg b\right) \vee \neg c$$
$$\neg \left(c \vee \neg a\right) = a \wedge \neg c$$
$$\neg \left(c \vee \neg b\right) = b \wedge \neg c$$
$$\neg \left(a \vee b\right) \vee \neg \left(c \vee \neg a\right) \vee \neg \left(c \vee \neg b\right) = \left(\neg a \wedge \neg b\right) \vee \neg c$$
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 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+
FNCD
[src]
$$\left(\neg a \vee \neg c\right) \wedge \left(\neg b \vee \neg c\right)$$
((¬a)∨(¬c))∧((¬b)∨(¬c))
FNC
[src]
$$\left(\neg a \vee \neg c\right) \wedge \left(\neg b \vee \neg c\right)$$
((¬a)∨(¬c))∧((¬b)∨(¬c))