Sr Examen
Expresión (¬av¬b)∧(b∧(avc)va∧c)∧(av(b∧¬c)v(c∧¬b))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬a)∨(¬b))∧((a∧c)∨(b∧(a∨c)))∧(a∨(b∧(¬c))∨(c∧(¬b)))
$$\left(\left(a \wedge c\right) \vee \left(b \wedge \left(a \vee c\right)\right)\right) \wedge \left(\neg a \vee \neg b\right) \wedge \left(a \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)\right)$$
Solución detallada
$$\left(a \wedge c\right) \vee \left(b \wedge \left(a \vee c\right)\right) = \left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right)$$
$$\left(\left(a \wedge c\right) \vee \left(b \wedge \left(a \vee c\right)\right)\right) \wedge \left(\neg a \vee \neg b\right) \wedge \left(a \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)\right) = a \wedge c \wedge \neg b$$
$$\left(\left(a \wedge c\right) \vee \left(b \wedge \left(a \vee c\right)\right)\right) \wedge \left(\neg a \vee \neg b\right) \wedge \left(a \vee \left(b \wedge \neg c\right) \vee \left(c \wedge \neg b\right)\right) = a \wedge c \wedge \neg b$$
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 | +---+---+---+--------+