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Expresión ¬((¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C))))
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Solución
Ha introducido
[src]
¬((¬(c∧(a∨b)))∨(¬(¬((a∧b)∨(b∧c)))))
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right)\right)$$
Solución detallada
$$\neg \left(c \wedge \left(a \vee b\right)\right) = \left(\neg a \wedge \neg b\right) \vee \neg c$$
$$\left(a \wedge b\right) \vee \left(b \wedge c\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right) = \left(\neg a \wedge \neg c\right) \vee \neg b$$
$$\neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(c \wedge \left(a \vee b\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = b \vee \neg a \vee \neg c$$
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right)\right) = a \wedge c \wedge \neg b$$
$$\left(a \wedge b\right) \vee \left(b \wedge c\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right) = \left(\neg a \wedge \neg c\right) \vee \neg b$$
$$\neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(c \wedge \left(a \vee b\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = b \vee \neg a \vee \neg c$$
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right)\right) = a \wedge c \wedge \neg b$$
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 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+