Sr Examen
Expresión av(b&c&cv(avc))=(avb)&(avc)
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Solución
Ha introducido
[src]
(a∨c∨(b∧c))⇔((a∨b)∧(a∨c))
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee c \vee \left(b \wedge c\right)\right)$$
Solución detallada
$$a \vee c \vee \left(b \wedge c\right) = a \vee c$$
$$\left(a \vee b\right) \wedge \left(a \vee c\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee c \vee \left(b \wedge c\right)\right) = a \vee b \vee \neg c$$
$$\left(a \vee b\right) \wedge \left(a \vee c\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) ⇔ \left(a \vee c \vee \left(b \wedge c\right)\right) = a \vee b \vee \neg c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+