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