Sr Examen
Lógica matemática/ (!a*b)+(a*!b*!c*!d*b)+(!a*!b*!c)+(!a*!c)+(!b+!a*!b*!c+!b)*(b*c*d+b*!c+b*c*!d)+(!a*c*!d)+(!a*!b*c)+(!a*c*d)+(!a*b)+(!a*!b*!c)

Expresión (!a*b)+(a*!b*!c*!d*b)+(!a*!b*!c)+(!a*!c)+(!b+!a*!b*!c+!b)*(b*c*d+b*!c+b*c*!d)+(!a*c*!d)+(!a*!b*c)+(!a*c*d)+(!a*b)+(!a*!b*!c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (b∧(¬a))∨((¬a)∧(¬c))∨(c∧d∧(¬a))∨(c∧(¬a)∧(¬b))∨(c∧(¬a)∧(¬d))∨((¬a)∧(¬b)∧(¬c))∨(a∧b∧(¬b)∧(¬c)∧(¬d))∨((b∨(¬b)∨(a∧(¬b)∧(¬c)))∧((b∧(¬c))∨(b∧c∧d)∨(b∧c∧(¬d))))
    $$\left(b \wedge \neg a\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(\left(b \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \neg b\right) \wedge \left(\left(b \wedge \neg c\right) \vee \left(b \wedge c \wedge d\right) \vee \left(b \wedge c \wedge \neg d\right)\right)\right) \vee \left(c \wedge d \wedge \neg a\right) \vee \left(c \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg d\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge \neg b \wedge \neg c \wedge \neg d\right)$$
    Solución detallada
    $$a \wedge b \wedge \neg b \wedge \neg c \wedge \neg d = \text{False}$$
    $$b \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \neg b = 1$$
    $$\left(b \wedge \neg c\right) \vee \left(b \wedge c \wedge d\right) \vee \left(b \wedge c \wedge \neg d\right) = b$$
    $$\left(b \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \neg b\right) \wedge \left(\left(b \wedge \neg c\right) \vee \left(b \wedge c \wedge d\right) \vee \left(b \wedge c \wedge \neg d\right)\right) = b$$
    $$\left(b \wedge \neg a\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(\left(b \vee \left(a \wedge \neg b \wedge \neg c\right) \vee \neg b\right) \wedge \left(\left(b \wedge \neg c\right) \vee \left(b \wedge c \wedge d\right) \vee \left(b \wedge c \wedge \neg d\right)\right)\right) \vee \left(c \wedge d \wedge \neg a\right) \vee \left(c \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg d\right) \vee \left(\neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge \neg b \wedge \neg c \wedge \neg d\right) = b \vee \neg a$$
    Simplificación [src]
    $$b \vee \neg a$$ 
    b∨(¬a)
    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 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 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 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FND [src]
    Ya está reducido a FND
    $$b \vee \neg a$$ 
    b∨(¬a)
    FNC [src]
    Ya está reducido a FNC
    $$b \vee \neg a$$ 
    b∨(¬a)
    FNDP [src]
    $$b \vee \neg a$$ 
    b∨(¬a)
    FNCD [src]
    $$b \vee \neg a$$ 
    b∨(¬a)
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