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