Sr Examen
Expresión ¬((¬(a∨b)∧c)∨(¬((a∧b)∧(b∧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))))
$$\neg \left(\left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(a \wedge b \wedge c\right)\right)$$
Solución detallada
$$\neg \left(a \wedge b \wedge c\right) = \neg a \vee \neg b \vee \neg c$$
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$c \wedge \neg \left(a \vee b\right) = c \wedge \neg a \wedge \neg b$$
$$\left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(a \wedge b \wedge c\right) = \neg a \vee \neg b \vee \neg c$$
$$\neg \left(\left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(a \wedge b \wedge c\right)\right) = a \wedge b \wedge c$$
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$c \wedge \neg \left(a \vee b\right) = c \wedge \neg a \wedge \neg b$$
$$\left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(a \wedge b \wedge c\right) = \neg a \vee \neg b \vee \neg c$$
$$\neg \left(\left(c \wedge \neg \left(a \vee b\right)\right) \vee \neg \left(a \wedge b \wedge c\right)\right) = a \wedge b \wedge c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+