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