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