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