Sr Examen
Expresión xy∨(¯(x→x¬y)→z)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(x∧y)∨(¬((x⇒(x∧(¬y)))⇒z))
$$\left(x \wedge y\right) \vee \left(x \Rightarrow \left(x \wedge \neg y\right)\right) \not\Rightarrow z$$
Solución detallada
$$x \Rightarrow \left(x \wedge \neg y\right) = \neg x \vee \neg y$$
$$\left(x \Rightarrow \left(x \wedge \neg y\right)\right) \Rightarrow z = z \vee \left(x \wedge y\right)$$
$$\left(x \Rightarrow \left(x \wedge \neg y\right)\right) \not\Rightarrow z = \neg z \wedge \left(\neg x \vee \neg y\right)$$
$$\left(x \wedge y\right) \vee \left(x \Rightarrow \left(x \wedge \neg y\right)\right) \not\Rightarrow z = \left(x \wedge y\right) \vee \neg z$$
$$\left(x \Rightarrow \left(x \wedge \neg y\right)\right) \Rightarrow z = z \vee \left(x \wedge y\right)$$
$$\left(x \Rightarrow \left(x \wedge \neg y\right)\right) \not\Rightarrow z = \neg z \wedge \left(\neg x \vee \neg y\right)$$
$$\left(x \wedge y\right) \vee \left(x \Rightarrow \left(x \wedge \neg y\right)\right) \not\Rightarrow z = \left(x \wedge y\right) \vee \neg z$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+