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