Sr Examen
Lógica matemática/ ((¬(a⊕b)∨¬b)∧c)⊕(¬(c∨d))

Expresión ((¬(a⊕b)∨¬b)∧c)⊕(¬(c∨d))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (¬(c∨d))⊕(c∧((¬b)∨(¬(a⊕b))))
    ¬(c∨d)⊕(c∧(¬b∨¬(a⊕b)))\neg \left(c \vee d\right) ⊕ \left(c \wedge \left(\neg b \vee \neg \left(a ⊕ b\right)\right)\right)
    Solución detallada
    ¬(c∨d)=¬c∧¬d\neg \left(c \vee d\right) = \neg c \wedge \neg d
    a⊕b=(a∧¬b)∨(b∧¬a)a ⊕ b = \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right)
    ¬(a⊕b)=(a∧b)∨(¬a∧¬b)\neg \left(a ⊕ b\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)
    ¬b∨¬(a⊕b)=a∨¬b\neg b \vee \neg \left(a ⊕ b\right) = a \vee \neg b
    c∧(¬b∨¬(a⊕b))=c∧(a∨¬b)c \wedge \left(\neg b \vee \neg \left(a ⊕ b\right)\right) = c \wedge \left(a \vee \neg b\right)
    ¬(c∨d)⊕(c∧(¬b∨¬(a⊕b)))=(a∧c)∨(c∧¬b)∨(¬c∧¬d)\neg \left(c \vee d\right) ⊕ \left(c \wedge \left(\neg b \vee \neg \left(a ⊕ b\right)\right)\right) = \left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(\neg c \wedge \neg d\right)
    Simplificación [src]
    (a∧c)∨(c∧¬b)∨(¬c∧¬d)\left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(\neg c \wedge \neg d\right) 
    (a∧c)∨(c∧(¬b))∨((¬c)∧(¬d))
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNDP [src]
    (a∧c)∨(c∧¬b)∨(¬c∧¬d)\left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(\neg c \wedge \neg d\right) 
    (a∧c)∨(c∧(¬b))∨((¬c)∧(¬d))
    FNCD [src]
    (c∨¬d)∧(a∨¬b∨¬c)\left(c \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg c\right) 
    (c∨(¬d))∧(a∨(¬b)∨(¬c))
    FNC [src]
    (c∨¬c)∧(c∨¬d)∧(a∨c∨¬c)∧(a∨c∨¬d)∧(a∨¬b∨¬c)∧(a∨¬b∨¬d)∧(c∨¬b∨¬c)∧(c∨¬b∨¬d)\left(c \vee \neg c\right) \wedge \left(c \vee \neg d\right) \wedge \left(a \vee c \vee \neg c\right) \wedge \left(a \vee c \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg c\right) \wedge \left(a \vee \neg b \vee \neg d\right) \wedge \left(c \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg b \vee \neg d\right) 
    (c∨(¬c))∧(c∨(¬d))∧(a∨c∨(¬c))∧(a∨c∨(¬d))∧(a∨(¬b)∨(¬c))∧(a∨(¬b)∨(¬d))∧(c∨(¬b)∨(¬c))∧(c∨(¬b)∨(¬d))
    FND [src]
    Ya está reducido a FND
    (a∧c)∨(c∧¬b)∨(¬c∧¬d)\left(a \wedge c\right) \vee \left(c \wedge \neg b\right) \vee \left(\neg c \wedge \neg d\right) 
    (a∧c)∨(c∧(¬b))∨((¬c)∧(¬d))
    © Sr Examen – Калькулятор