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