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