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