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