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