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