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