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