Sr Examen
Lógica matemática/ (bvcvd)⇒d(avb)va(b⇔d)

Expresión (bvcvd)⇒d(avb)va(b⇔d)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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