Sr Examen
Expresión ¬(¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C)))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(¬(c∧(a∨b))))∨(¬(¬((a∧b)∨(b∧c))))
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right)$$
Solución detallada
$$\neg \left(c \wedge \left(a \vee b\right)\right) = \left(\neg a \wedge \neg b\right) \vee \neg c$$
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right)\right) = c \wedge \left(a \vee b\right)$$
$$\left(a \wedge b\right) \vee \left(b \wedge c\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right) = \left(\neg a \wedge \neg c\right) \vee \neg b$$
$$\neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = \left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right)$$
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right)\right) = c \wedge \left(a \vee b\right)$$
$$\left(a \wedge b\right) \vee \left(b \wedge c\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right) = \left(\neg a \wedge \neg c\right) \vee \neg b$$
$$\neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = b \wedge \left(a \vee c\right)$$
$$\neg \left(\neg \left(c \wedge \left(a \vee b\right)\right)\right) \vee \neg \left(\neg \left(\left(a \wedge b\right) \vee \left(b \wedge c\right)\right)\right) = \left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right)$$
Simplificación
[src]
$$\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right)$$
(a∧b)∨(a∧c)∨(b∧c)
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNCD
[src]
$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(b \vee c\right)$$
(a∨b)∧(a∨c)∧(b∨c)
FNDP
[src]
$$\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right)$$
(a∧b)∨(a∧c)∨(b∧c)
FND
[src]
Ya está reducido a FND
$$\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right)$$
(a∧b)∨(a∧c)∨(b∧c)
FNC
[src]
$$\left(a \vee b\right) \wedge \left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(a \vee b \vee c\right)$$
(a∨b)∧(a∨c)∧(b∨c)∧(a∨b∨c)