Sr Examen
Expresión x⇒(y⇒z)⇒(x*(y⇒z))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(x⇒(y⇒z))⇒(x∧(y⇒z))
$$\left(x \Rightarrow \left(y \Rightarrow z\right)\right) \Rightarrow \left(x \wedge \left(y \Rightarrow z\right)\right)$$
Solución detallada
$$y \Rightarrow z = z \vee \neg y$$
$$x \Rightarrow \left(y \Rightarrow z\right) = z \vee \neg x \vee \neg y$$
$$x \wedge \left(y \Rightarrow z\right) = x \wedge \left(z \vee \neg y\right)$$
$$\left(x \Rightarrow \left(y \Rightarrow z\right)\right) \Rightarrow \left(x \wedge \left(y \Rightarrow z\right)\right) = x$$
$$x \Rightarrow \left(y \Rightarrow z\right) = z \vee \neg x \vee \neg y$$
$$x \wedge \left(y \Rightarrow z\right) = x \wedge \left(z \vee \neg y\right)$$
$$\left(x \Rightarrow \left(y \Rightarrow z\right)\right) \Rightarrow \left(x \wedge \left(y \Rightarrow z\right)\right) = x$$
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 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+