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Lógica matemática/ pvp2v¬(p2⊕p3)

Expresión pvp2v¬(p2⊕p3)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución

Ha introducido [src]

p∨p2∨(¬(p2⊕p3))

$$p \vee p_{2} \vee \neg \left(p_{2} ⊕ p_{3}\right)$$

Solución detallada

$$p_{2} ⊕ p_{3} = \left(p_{2} \wedge \neg p_{3}\right) \vee \left(p_{3} \wedge \neg p_{2}\right)$$
$$\neg \left(p_{2} ⊕ p_{3}\right) = \left(p_{2} \wedge p_{3}\right) \vee \left(\neg p_{2} \wedge \neg p_{3}\right)$$
$$p \vee p_{2} \vee \neg \left(p_{2} ⊕ p_{3}\right) = p \vee p_{2} \vee \neg p_{3}$$

Simplificación [src]

$$p \vee p_{2} \vee \neg p_{3}$$

p∨p2∨(¬p3)

Tabla de verdad

+---+----+----+--------+
| p | p2 | p3 | result |
+===+====+====+========+
| 0 | 0  | 0  | 1      |
+---+----+----+--------+
| 0 | 0  | 1  | 0      |
+---+----+----+--------+
| 0 | 1  | 0  | 1      |
+---+----+----+--------+
| 0 | 1  | 1  | 1      |
+---+----+----+--------+
| 1 | 0  | 0  | 1      |
+---+----+----+--------+
| 1 | 0  | 1  | 1      |
+---+----+----+--------+
| 1 | 1  | 0  | 1      |
+---+----+----+--------+
| 1 | 1  | 1  | 1      |
+---+----+----+--------+

FNDP [src]

$$p \vee p_{2} \vee \neg p_{3}$$

p∨p2∨(¬p3)

FNCD [src]

$$p \vee p_{2} \vee \neg p_{3}$$

p∨p2∨(¬p3)

FNC [src]

Ya está reducido a FNC

$$p \vee p_{2} \vee \neg p_{3}$$

p∨p2∨(¬p3)

FND [src]

Ya está reducido a FND

$$p \vee p_{2} \vee \neg p_{3}$$

p∨p2∨(¬p3)