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Lógica matemática/ not(A)*B*not(C)+A*B*not(D)+not(A)*D

Expresión not(A)*B*not(C)+A*B*not(D)+not(A)*D

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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