Sr Examen
Expresión (a∧¬(¬c∨¬b))∨(¬(¬a∨b)∧c)∨(a∧c)
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Solución
Ha introducido
[src]
(a∧c)∨(c∧(¬(b∨(¬a))))∨(a∧(¬((¬b)∨(¬c))))
$$\left(a \wedge c\right) \vee \left(a \wedge \neg \left(\neg b \vee \neg c\right)\right) \vee \left(c \wedge \neg \left(b \vee \neg a\right)\right)$$
Solución detallada
$$\neg \left(b \vee \neg a\right) = a \wedge \neg b$$
$$c \wedge \neg \left(b \vee \neg a\right) = a \wedge c \wedge \neg b$$
$$\neg \left(\neg b \vee \neg c\right) = b \wedge c$$
$$a \wedge \neg \left(\neg b \vee \neg c\right) = a \wedge b \wedge c$$
$$\left(a \wedge c\right) \vee \left(a \wedge \neg \left(\neg b \vee \neg c\right)\right) \vee \left(c \wedge \neg \left(b \vee \neg a\right)\right) = a \wedge c$$
$$c \wedge \neg \left(b \vee \neg a\right) = a \wedge c \wedge \neg b$$
$$\neg \left(\neg b \vee \neg c\right) = b \wedge c$$
$$a \wedge \neg \left(\neg b \vee \neg c\right) = a \wedge b \wedge c$$
$$\left(a \wedge c\right) \vee \left(a \wedge \neg \left(\neg b \vee \neg c\right)\right) \vee \left(c \wedge \neg \left(b \vee \neg a\right)\right) = a \wedge c$$
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 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+