Expresión (B⊕A)∧(¬(¬B∧¬C))
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$a ⊕ b = \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right)$$
$$\neg \left(\neg b \wedge \neg c\right) = b \vee c$$
$$\neg \left(\neg b \wedge \neg c\right) \wedge \left(a ⊕ b\right) = \left(a \vee b\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b\right)$$
$$\left(a \vee b\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b\right)$$
Tabla de verdad
+---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 0 |
+---+---+---+--------+
| 0 | 0 | 1 | 0 |
+---+---+---+--------+
| 0 | 1 | 0 | 1 |
+---+---+---+--------+
| 0 | 1 | 1 | 1 |
+---+---+---+--------+
| 1 | 0 | 0 | 0 |
+---+---+---+--------+
| 1 | 0 | 1 | 1 |
+---+---+---+--------+
| 1 | 1 | 0 | 0 |
+---+---+---+--------+
| 1 | 1 | 1 | 0 |
+---+---+---+--------+
Ya está reducido a FNC
$$\left(a \vee b\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b\right)$$
$$\left(a \vee b\right) \wedge \left(b \vee c\right) \wedge \left(\neg a \vee \neg b\right)$$
$$\left(b \wedge \neg a\right) \vee \left(a \wedge c \wedge \neg b\right)$$
$$\left(b \wedge \neg a\right) \vee \left(b \wedge \neg b\right) \vee \left(a \wedge b \wedge \neg a\right) \vee \left(a \wedge b \wedge \neg b\right) \vee \left(a \wedge c \wedge \neg a\right) \vee \left(a \wedge c \wedge \neg b\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \left(b \wedge c \wedge \neg b\right)$$
(b∧(¬a))∨(b∧(¬b))∨(a∧b∧(¬a))∨(a∧b∧(¬b))∨(a∧c∧(¬a))∨(a∧c∧(¬b))∨(b∧c∧(¬a))∨(b∧c∧(¬b))