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