|
|
|
|
|
|
|
|
|
|
|
|
Vereenvoudig $$$\left(\left(1 \cdot 0\right) + \overline{0}\right) \cdot \left(\overline{1} + 0 + 1\right)$$$
Gerelateerde rekenmachine: Waarheidstabel-rekenmachine
Uw invoer
Vereenvoudig de Booleaanse uitdrukking $$$\left(\left(1 \cdot 0\right) + \overline{0}\right) \cdot \left(\overline{1} + 0 + 1\right)$$$.
Oplossing
Pas de wet van de negatie $$$\overline{0} = 1$$$ toe:
$$\left(\left(1 \cdot 0\right) + {\color{red}\left(\overline{0}\right)}\right) \cdot \left(\overline{1} + 0 + 1\right) = \left(\left(1 \cdot 0\right) + {\color{red}\left(1\right)}\right) \cdot \left(\overline{1} + 0 + 1\right)$$Pas de wet van de negatie $$$\overline{1} = 0$$$ toe:
$$\left(\left(1 \cdot 0\right) + 1\right) \cdot \left({\color{red}\left(\overline{1}\right)} + 0 + 1\right) = \left(\left(1 \cdot 0\right) + 1\right) \cdot \left({\color{red}\left(0\right)} + 0 + 1\right)$$Pas de dominantiewet (nulwet, annuleringswet) $$$x + 1 = 1$$$ toe met $$$x = 1 \cdot 0$$$:
$${\color{red}\left(\left(1 \cdot 0\right) + 1\right)} \cdot \left(0 + 0 + 1\right) = {\color{red}\left(1\right)} \cdot \left(0 + 0 + 1\right)$$Pas de dominantiewet (nulwet, annuleringswet) $$$x + 1 = 1$$$ toe met $$$x = 0$$$:
$$1 \cdot \left(0 + {\color{red}\left(0 + 1\right)}\right) = 1 \cdot \left(0 + {\color{red}\left(1\right)}\right)$$Pas de dominantiewet (nulwet, annuleringswet) $$$x + 1 = 1$$$ toe met $$$x = 0$$$:
$$1 \cdot {\color{red}\left(0 + 1\right)} = 1 \cdot {\color{red}\left(1\right)}$$Pas de identiteitswet $$$x \cdot 1 = x$$$ toe met $$$x = 1$$$:
$${\color{red}\left(1 \cdot 1\right)} = {\color{red}\left(1\right)}$$Antwoord
$$$\left(\left(1 \cdot 0\right) + \overline{0}\right) \cdot \left(\overline{1} + 0 + 1\right) = 1$$$
De DNF is $$$\text{True}$$$.
De CNF is $$$\text{True}$$$.
De NNF is $$$\text{True}$$$.