Sr Examen
Expresión x=>yz(x->y)(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)∧(y⇒z))
$$x \Rightarrow \left(y \wedge z \wedge \left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right)\right)$$
Solución detallada
$$x \Rightarrow y = y \vee \neg x$$
$$y \Rightarrow z = z \vee \neg y$$
$$y \wedge z \wedge \left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right) = y \wedge z$$
$$x \Rightarrow \left(y \wedge z \wedge \left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right)\right) = \left(y \wedge z\right) \vee \neg x$$
$$y \Rightarrow z = z \vee \neg y$$
$$y \wedge z \wedge \left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right) = y \wedge z$$
$$x \Rightarrow \left(y \wedge z \wedge \left(x \Rightarrow y\right) \wedge \left(y \Rightarrow z\right)\right) = \left(y \wedge z\right) \vee \neg x$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+