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