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