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