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