Sr Examen
Expresión (¬aavb)&(avc)&(bvc)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(a∨c)∧(b∨c)∧(b∨(a∧(¬a)))
$$\left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(b \vee \left(a \wedge \neg a\right)\right)$$
Solución detallada
$$a \wedge \neg a = \text{False}$$
$$b \vee \left(a \wedge \neg a\right) = b$$
$$\left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(b \vee \left(a \wedge \neg a\right)\right) = b \wedge \left(a \vee c\right)$$
$$b \vee \left(a \wedge \neg a\right) = b$$
$$\left(a \vee c\right) \wedge \left(b \vee c\right) \wedge \left(b \vee \left(a \wedge \neg a\right)\right) = b \wedge \left(a \vee c\right)$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+