Sr Examen
Expresión (¬b⇒a∨c)⇒¬(a⇒b∧¬(c∨¬a))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬b)⇒(a∨c))⇒(¬(a⇒(b∧(¬(c∨(¬a))))))
$$\left(\neg b \Rightarrow \left(a \vee c\right)\right) \Rightarrow a \not\Rightarrow \left(b \wedge \neg \left(c \vee \neg a\right)\right)$$
Solución detallada
$$\neg b \Rightarrow \left(a \vee c\right) = a \vee b \vee c$$
$$\neg \left(c \vee \neg a\right) = a \wedge \neg c$$
$$b \wedge \neg \left(c \vee \neg a\right) = a \wedge b \wedge \neg c$$
$$a \Rightarrow \left(b \wedge \neg \left(c \vee \neg a\right)\right) = \left(b \wedge \neg c\right) \vee \neg a$$
$$a \not\Rightarrow \left(b \wedge \neg \left(c \vee \neg a\right)\right) = a \wedge \left(c \vee \neg b\right)$$
$$\left(\neg b \Rightarrow \left(a \vee c\right)\right) \Rightarrow a \not\Rightarrow \left(b \wedge \neg \left(c \vee \neg a\right)\right) = \left(a \wedge c\right) \vee \left(\neg b \wedge \neg c\right)$$
$$\neg \left(c \vee \neg a\right) = a \wedge \neg c$$
$$b \wedge \neg \left(c \vee \neg a\right) = a \wedge b \wedge \neg c$$
$$a \Rightarrow \left(b \wedge \neg \left(c \vee \neg a\right)\right) = \left(b \wedge \neg c\right) \vee \neg a$$
$$a \not\Rightarrow \left(b \wedge \neg \left(c \vee \neg a\right)\right) = a \wedge \left(c \vee \neg b\right)$$
$$\left(\neg b \Rightarrow \left(a \vee c\right)\right) \Rightarrow a \not\Rightarrow \left(b \wedge \neg \left(c \vee \neg a\right)\right) = \left(a \wedge c\right) \vee \left(\neg b \wedge \neg c\right)$$
Simplificación
[src]
$$\left(a \wedge c\right) \vee \left(\neg b \wedge \neg c\right)$$
(a∧c)∨((¬b)∧(¬c))
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+
FNC
[src]
$$\left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(c \vee \neg b\right) \wedge \left(c \vee \neg c\right)$$
(a∨(¬b))∧(a∨(¬c))∧(c∨(¬b))∧(c∨(¬c))
FND
[src]
Ya está reducido a FND
$$\left(a \wedge c\right) \vee \left(\neg b \wedge \neg c\right)$$
(a∧c)∨((¬b)∧(¬c))