Sr Examen
Expresión A&¬(BVC)VA&BVA&C
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Solución
Ha introducido
[src]
(a∧b)∨(a∧c)∨(a∧(¬(b∨c)))
$$\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(a \wedge \neg \left(b \vee c\right)\right)$$
Solución detallada
$$\neg \left(b \vee c\right) = \neg b \wedge \neg c$$
$$a \wedge \neg \left(b \vee c\right) = a \wedge \neg b \wedge \neg c$$
$$\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(a \wedge \neg \left(b \vee c\right)\right) = a$$
$$a \wedge \neg \left(b \vee c\right) = a \wedge \neg b \wedge \neg c$$
$$\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(a \wedge \neg \left(b \vee c\right)\right) = a$$
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 | +---+---+---+--------+