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

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

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