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