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