Expresión ¬B&Av(¬A&B)&(¬BvA)vA&B=B
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$b \wedge \neg a \wedge \left(a \vee \neg b\right) = \text{False}$$
$$\left(a \wedge b\right) \vee \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a \wedge \left(a \vee \neg b\right)\right) = a$$
$$b ⇔ \left(\left(a \wedge b\right) \vee \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a \wedge \left(a \vee \neg b\right)\right)\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
Tabla de verdad
+---+---+--------+
| a | b | result |
+===+===+========+
| 0 | 0 | 1 |
+---+---+--------+
| 0 | 1 | 0 |
+---+---+--------+
| 1 | 0 | 0 |
+---+---+--------+
| 1 | 1 | 1 |
+---+---+--------+
Ya está reducido a FND
$$\left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(a \vee \neg b\right) \wedge \left(b \vee \neg a\right)$$
$$\left(a \vee \neg a\right) \wedge \left(a \vee \neg b\right) \wedge \left(b \vee \neg a\right) \wedge \left(b \vee \neg b\right)$$
(a∨(¬a))∧(a∨(¬b))∧(b∨(¬a))∧(b∨(¬b))
$$\left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$