Sr Examen
Expresión ¬(a*b+c*d)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
¬((a∧b)∨(c∧d))
$$\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right)$$
Solución detallada
$$\left(a \wedge b\right) \vee \left(c \wedge d\right) = \left(a \vee c\right) \wedge \left(a \vee d\right) \wedge \left(b \vee c\right) \wedge \left(b \vee d\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) = \left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
$$\neg \left(\left(a \wedge b\right) \vee \left(c \wedge d\right)\right) = \left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
Simplificación
[src]
$$\left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
((¬a)∧(¬c))∨((¬a)∧(¬d))∨((¬b)∧(¬c))∨((¬b)∧(¬d))
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 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+
FNDP
[src]
$$\left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
((¬a)∧(¬c))∨((¬a)∧(¬d))∨((¬b)∧(¬c))∨((¬b)∧(¬d))
FND
[src]
Ya está reducido a FND
$$\left(\neg a \wedge \neg c\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
((¬a)∧(¬c))∨((¬a)∧(¬d))∨((¬b)∧(¬c))∨((¬b)∧(¬d))
FNCD
[src]
$$\left(\neg a \vee \neg b\right) \wedge \left(\neg c \vee \neg d\right)$$
((¬a)∨(¬b))∧((¬c)∨(¬d))
FNC
[src]
$$\left(\neg a \vee \neg b\right) \wedge \left(\neg c \vee \neg d\right) \wedge \left(\neg a \vee \neg b \vee \neg c\right) \wedge \left(\neg a \vee \neg b \vee \neg d\right) \wedge \left(\neg a \vee \neg c \vee \neg d\right) \wedge \left(\neg b \vee \neg c \vee \neg d\right) \wedge \left(\neg a \vee \neg b \vee \neg c \vee \neg d\right)$$
((¬a)∨(¬b))∧((¬c)∨(¬d))∧((¬a)∨(¬b)∨(¬c))∧((¬a)∨(¬b)∨(¬d))∧((¬a)∨(¬c)∨(¬d))∧((¬b)∨(¬c)∨(¬d))∧((¬a)∨(¬b)∨(¬c)∨(¬d))