Sr Examen
Expresión not(x&y+notz)&(notx+noty+z)+(notx+z)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
z∨(¬x)∨((z∨(¬x)∨(¬y))∧(¬((¬z)∨(x∧y))))
$$z \vee \left(\neg \left(\left(x \wedge y\right) \vee \neg z\right) \wedge \left(z \vee \neg x \vee \neg y\right)\right) \vee \neg x$$
Solución detallada
$$\neg \left(\left(x \wedge y\right) \vee \neg z\right) = z \wedge \left(\neg x \vee \neg y\right)$$
$$\neg \left(\left(x \wedge y\right) \vee \neg z\right) \wedge \left(z \vee \neg x \vee \neg y\right) = z \wedge \left(\neg x \vee \neg y\right)$$
$$z \vee \left(\neg \left(\left(x \wedge y\right) \vee \neg z\right) \wedge \left(z \vee \neg x \vee \neg y\right)\right) \vee \neg x = z \vee \neg x$$
$$\neg \left(\left(x \wedge y\right) \vee \neg z\right) \wedge \left(z \vee \neg x \vee \neg y\right) = z \wedge \left(\neg x \vee \neg y\right)$$
$$z \vee \left(\neg \left(\left(x \wedge y\right) \vee \neg z\right) \wedge \left(z \vee \neg x \vee \neg y\right)\right) \vee \neg x = z \vee \neg x$$
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 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+