Sr Examen
Lógica matemática/ AC+B'CD'+BCD+AB'D'+ABD+A'B'C'D+A'BC'D'

Expresión AC+B'CD'+BCD+AB'D'+ABD+A'B'C'D+A'BC'D'

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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