Sr Examen
Expresión A⇔(B∧C)
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Solución
Solución detallada
$$a ⇔ \left(b \wedge c\right) = \left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
Simplificación
[src]
$$\left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
(a∧b∧c)∨((¬a)∧(¬b))∨((¬a)∧(¬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 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNCD
[src]
$$\left(b \vee \neg a\right) \wedge \left(c \vee \neg a\right) \wedge \left(a \vee \neg b \vee \neg c\right)$$
(b∨(¬a))∧(c∨(¬a))∧(a∨(¬b)∨(¬c))
FND
[src]
Ya está reducido a FND
$$\left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
(a∧b∧c)∨((¬a)∧(¬b))∨((¬a)∧(¬c))
FNC
[src]
$$\left(a \vee \neg a\right) \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg a\right) \wedge \left(a \vee \neg a \vee \neg b\right) \wedge \left(a \vee \neg a \vee \neg c\right) \wedge \left(a \vee \neg b \vee \neg c\right) \wedge \left(b \vee \neg a \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg c\right) \wedge \left(b \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg b \vee \neg c\right)$$
(a∨(¬a))∧(b∨(¬a))∧(c∨(¬a))∧(a∨(¬a)∨(¬b))∧(a∨(¬a)∨(¬c))∧(a∨(¬b)∨(¬c))∧(b∨(¬a)∨(¬b))∧(b∨(¬a)∨(¬c))∧(b∨(¬b)∨(¬c))∧(c∨(¬a)∨(¬b))∧(c∨(¬a)∨(¬c))∧(c∨(¬b)∨(¬c))
FNDP
[src]
$$\left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
(a∧b∧c)∨((¬a)∧(¬b))∨((¬a)∧(¬c))