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Lógica matemática/ —F=¬(((¬X1)=⇒X2)=⇒(X3=⇒X4))

Expresión —F=¬(((¬X1)=⇒X2)=⇒(X3=⇒X4))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    ¬(f⇔(¬((True)⇒((True)⇒x4))))
    $$f \not\equiv \left(\text{True}\right) \not\Rightarrow \left(\left(\text{True}\right) \Rightarrow x_{4}\right)$$
    Solución detallada
    $$\left(\text{True}\right) \Rightarrow x_{4} = x_{4}$$
    $$\left(\text{True}\right) \Rightarrow \left(\left(\text{True}\right) \Rightarrow x_{4}\right) = x_{4}$$
    $$\left(\text{True}\right) \not\Rightarrow \left(\left(\text{True}\right) \Rightarrow x_{4}\right) = \neg x_{4}$$
    $$f ⇔ \left(\text{True}\right) \not\Rightarrow \left(\left(\text{True}\right) \Rightarrow x_{4}\right) = \left(f \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge \neg f\right)$$
    $$f \not\equiv \left(\text{True}\right) \not\Rightarrow \left(\left(\text{True}\right) \Rightarrow x_{4}\right) = \left(f \wedge x_{4}\right) \vee \left(\neg f \wedge \neg x_{4}\right)$$
    Simplificación [src]
    $$\left(f \wedge x_{4}\right) \vee \left(\neg f \wedge \neg x_{4}\right)$$ 
    (f∧x4)∨((¬f)∧(¬x4))
    Tabla de verdad 
    +---+----+--------+
| f | x4 | result |
+===+====+========+
| 0 | 0  | 1      |
+---+----+--------+
| 0 | 1  | 0      |
+---+----+--------+
| 1 | 0  | 0      |
+---+----+--------+
| 1 | 1  | 1      |
+---+----+--------+
    FND [src]
    Ya está reducido a FND
    $$\left(f \wedge x_{4}\right) \vee \left(\neg f \wedge \neg x_{4}\right)$$ 
    (f∧x4)∨((¬f)∧(¬x4))
    FNDP [src]
    $$\left(f \wedge x_{4}\right) \vee \left(\neg f \wedge \neg x_{4}\right)$$ 
    (f∧x4)∨((¬f)∧(¬x4))
    FNC [src]
    $$\left(f \vee \neg f\right) \wedge \left(f \vee \neg x_{4}\right) \wedge \left(x_{4} \vee \neg f\right) \wedge \left(x_{4} \vee \neg x_{4}\right)$$ 
    (f∨(¬f))∧(f∨(¬x4))∧(x4∨(¬f))∧(x4∨(¬x4))
    FNCD [src]
    $$\left(f \vee \neg x_{4}\right) \wedge \left(x_{4} \vee \neg f\right)$$ 
    (f∨(¬x4))∧(x4∨(¬f))
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