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