Sr Examen
Expresión av(b/c)=(avb)&(avc)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(a∨(b|c))⇔((a∨b)∧(a∨c))
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee \left(b | c\right)\right)$$
Solución detallada
$$b | c = \neg b \vee \neg c$$
$$a \vee \left(b | c\right) = a \vee \neg b \vee \neg c$$
$$\left(a \vee b\right) \wedge \left(a \vee c\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee \left(b | c\right)\right) = a$$
$$a \vee \left(b | c\right) = a \vee \neg b \vee \neg c$$
$$\left(a \vee b\right) \wedge \left(a \vee c\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee \left(b | c\right)\right) = a$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+