Sr Examen
Expresión (notA)and(notB)and(not(A+notB))+(AB)and(not(A+B))
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Solución
Ha introducido
[src]
(a∧b∧(¬(a∨b)))∨((¬a)∧(¬b)∧(¬(a∨(¬b))))
$$\left(a \wedge b \wedge \neg \left(a \vee b\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg \left(a \vee \neg b\right)\right)$$
Solución detallada
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$a \wedge b \wedge \neg \left(a \vee b\right) = \text{False}$$
$$\neg \left(a \vee \neg b\right) = b \wedge \neg a$$
$$\neg a \wedge \neg b \wedge \neg \left(a \vee \neg b\right) = \text{False}$$
$$\left(a \wedge b \wedge \neg \left(a \vee b\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg \left(a \vee \neg b\right)\right) = \text{False}$$
$$a \wedge b \wedge \neg \left(a \vee b\right) = \text{False}$$
$$\neg \left(a \vee \neg b\right) = b \wedge \neg a$$
$$\neg a \wedge \neg b \wedge \neg \left(a \vee \neg b\right) = \text{False}$$
$$\left(a \wedge b \wedge \neg \left(a \vee b\right)\right) \vee \left(\neg a \wedge \neg b \wedge \neg \left(a \vee \neg b\right)\right) = \text{False}$$
Tabla de verdad
+---+---+--------+ | a | b | result | +===+===+========+ | 0 | 0 | 0 | +---+---+--------+ | 0 | 1 | 0 | +---+---+--------+ | 1 | 0 | 0 | +---+---+--------+ | 1 | 1 | 0 | +---+---+--------+