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