Sr Examen
Lógica matemática/ x((uvb)&xvy(zv!xvyvcv!x&y))v!x&y&(av!a&x)

Expresión x((uvb)&xvy(zv!xvyvcv!x&y))v!x&y&(av!a&x)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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