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