Expresión ac∨¬a¬b¬c
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Solución
Solución detallada
$$\left(a \wedge c\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right) = \left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$
$$\left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$
(a∨(¬c))∧(c∨(¬a))∧(c∨(¬b))
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 | 0 |
+---+---+---+--------+
| 1 | 0 | 1 | 1 |
+---+---+---+--------+
| 1 | 1 | 0 | 0 |
+---+---+---+--------+
| 1 | 1 | 1 | 1 |
+---+---+---+--------+
$$\left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$
(a∨(¬c))∧(c∨(¬a))∧(c∨(¬b))
$$\left(a \wedge c\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right)$$
Ya está reducido a FNC
$$\left(a \vee \neg c\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$
(a∨(¬c))∧(c∨(¬a))∧(c∨(¬b))
$$\left(a \wedge c\right) \vee \left(c \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg a\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \left(a \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg c\right) \vee \left(c \wedge \neg b \wedge \neg c\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right)$$
(a∧c)∨(c∧(¬c))∨(a∧c∧(¬a))∨(a∧c∧(¬b))∨(a∧(¬a)∧(¬b))∨(c∧(¬a)∧(¬c))∨(c∧(¬b)∧(¬c))∨((¬a)∧(¬b)∧(¬c))