Sr Examen
Expresión ¬(¬A∧¬B∧C)∧¬(¬A∧B)∧¬A∧C
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
c∧(¬a)∧(¬(b∧(¬a)))∧(¬(c∧(¬a)∧(¬b)))
$$c \wedge \neg a \wedge \neg \left(b \wedge \neg a\right) \wedge \neg \left(c \wedge \neg a \wedge \neg b\right)$$
Solución detallada
$$\neg \left(b \wedge \neg a\right) = a \vee \neg b$$
$$\neg \left(c \wedge \neg a \wedge \neg b\right) = a \vee b \vee \neg c$$
$$c \wedge \neg a \wedge \neg \left(b \wedge \neg a\right) \wedge \neg \left(c \wedge \neg a \wedge \neg b\right) = \text{False}$$
$$\neg \left(c \wedge \neg a \wedge \neg b\right) = a \vee b \vee \neg c$$
$$c \wedge \neg a \wedge \neg \left(b \wedge \neg a\right) \wedge \neg \left(c \wedge \neg a \wedge \neg b\right) = \text{False}$$
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 | 0 | +---+---+---+--------+