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