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