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