Sr Examen
Expresión (x+y)(¬x+¬(x+y))+xy
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Solución
Ha introducido
[src]
(x∧y)∨((x∨y)∧((¬x)∨(¬(x∨y))))
$$\left(x \wedge y\right) \vee \left(\left(x \vee y\right) \wedge \left(\neg x \vee \neg \left(x \vee y\right)\right)\right)$$
Solución detallada
$$\neg \left(x \vee y\right) = \neg x \wedge \neg y$$
$$\neg x \vee \neg \left(x \vee y\right) = \neg x$$
$$\left(x \vee y\right) \wedge \left(\neg x \vee \neg \left(x \vee y\right)\right) = y \wedge \neg x$$
$$\left(x \wedge y\right) \vee \left(\left(x \vee y\right) \wedge \left(\neg x \vee \neg \left(x \vee y\right)\right)\right) = y$$
$$\neg x \vee \neg \left(x \vee y\right) = \neg x$$
$$\left(x \vee y\right) \wedge \left(\neg x \vee \neg \left(x \vee y\right)\right) = y \wedge \neg x$$
$$\left(x \wedge y\right) \vee \left(\left(x \vee y\right) \wedge \left(\neg x \vee \neg \left(x \vee y\right)\right)\right) = y$$
Tabla de verdad
+---+---+--------+ | x | y | result | +===+===+========+ | 0 | 0 | 0 | +---+---+--------+ | 0 | 1 | 1 | +---+---+--------+ | 1 | 0 | 0 | +---+---+--------+ | 1 | 1 | 1 | +---+---+--------+