Sr Examen
Lógica matemática/ ab¬cd+a¬b¬c¬d+¬a¬b¬c¬d+abcd+a¬bcd+¬abc¬d+¬abcd+¬ab¬c¬d+¬ab¬cd+¬a¬b¬cd

Expresión ab¬cd+a¬b¬c¬d+¬a¬b¬c¬d+abcd+a¬bcd+¬abc¬d+¬abcd+¬ab¬c¬d+¬ab¬cd+¬a¬b¬cd

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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