Sr Examen
Expresión a&b&(b&cv!c)va&c(a&b)
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Solución
Ha introducido
[src]
(a∧b∧c)∨(a∧b∧((¬c)∨(b∧c)))
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \left(\left(b \wedge c\right) \vee \neg c\right)\right)$$
Solución detallada
$$\left(b \wedge c\right) \vee \neg c = b \vee \neg c$$
$$a \wedge b \wedge \left(\left(b \wedge c\right) \vee \neg c\right) = a \wedge b$$
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \left(\left(b \wedge c\right) \vee \neg c\right)\right) = a \wedge b$$
$$a \wedge b \wedge \left(\left(b \wedge c\right) \vee \neg c\right) = a \wedge b$$
$$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge \left(\left(b \wedge c\right) \vee \neg c\right)\right) = a \wedge b$$
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 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+