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