Sr Examen
Expresión ¬(¬(AB)C)∨¬(A∨¬B)¬C
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Solución
Ha introducido
[src]
(¬(c∧(¬(a∧b))))∨((¬c)∧(¬(a∨(¬b))))
$$\left(\neg c \wedge \neg \left(a \vee \neg b\right)\right) \vee \neg \left(c \wedge \neg \left(a \wedge b\right)\right)$$
Solución detallada
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$c \wedge \neg \left(a \wedge b\right) = c \wedge \left(\neg a \vee \neg b\right)$$
$$\neg \left(c \wedge \neg \left(a \wedge b\right)\right) = \left(a \wedge b\right) \vee \neg c$$
$$\neg \left(a \vee \neg b\right) = b \wedge \neg a$$
$$\neg c \wedge \neg \left(a \vee \neg b\right) = b \wedge \neg a \wedge \neg c$$
$$\left(\neg c \wedge \neg \left(a \vee \neg b\right)\right) \vee \neg \left(c \wedge \neg \left(a \wedge b\right)\right) = \left(a \wedge b\right) \vee \neg c$$
$$c \wedge \neg \left(a \wedge b\right) = c \wedge \left(\neg a \vee \neg b\right)$$
$$\neg \left(c \wedge \neg \left(a \wedge b\right)\right) = \left(a \wedge b\right) \vee \neg c$$
$$\neg \left(a \vee \neg b\right) = b \wedge \neg a$$
$$\neg c \wedge \neg \left(a \vee \neg b\right) = b \wedge \neg a \wedge \neg c$$
$$\left(\neg c \wedge \neg \left(a \vee \neg b\right)\right) \vee \neg \left(c \wedge \neg \left(a \wedge b\right)\right) = \left(a \wedge b\right) \vee \neg c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+