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