Expresión P→(Q→(R∧S→P))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

Solución

Ha introducido [src]

p⇒(q⇒((r∧s)⇒p))

p \Rightarrow \left(q \Rightarrow \left(\left(r \wedge s\right) \Rightarrow p\right)\right)

Solución detallada

\left(r \wedge s\right) \Rightarrow p = p \vee \neg r \vee \neg s

q \Rightarrow \left(\left(r \wedge s\right) \Rightarrow p\right) = p \vee \neg q \vee \neg r \vee \neg s

p \Rightarrow \left(q \Rightarrow \left(\left(r \wedge s\right) \Rightarrow p\right)\right) = 1

Simplificación [src]

Tabla de verdad

+---+---+---+---+--------+
| p | q | r | s | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+

FNDP [src]

FNCD [src]

FNC [src]

Ya está reducido a FNC

FND [src]

Ya está reducido a FND

¿Cómo usar?

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Expresión P→(Q→(R∧S→P))

Solución