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