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