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