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Expresiones idénticas
NOT(x)*x3*x4+x uno *x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x) multiplicar por x3 multiplicar por x4 más x1 multiplicar por x multiplicar por x5 más x3 multiplicar por x1 multiplicar por NOT(x4) multiplicar por NOT(x1) más x2 multiplicar por x4 más NOT(x2) multiplicar por NOT(x3) multiplicar por x4 más x2 multiplicar por x4 más (x1 multiplicar por x multiplicar por x3 más 1) multiplicar por (NOT(x1) multiplicar por NOT(x3) más NOT(x1) multiplicar por x3 multiplicar por x4 más NOT(x1) multiplicar por x3 multiplicar por NOT(x4) más NOT(x1) multiplicar por NOT(x3)) más NOT(x1 multiplicar por x2) más x1 multiplicar por x2 multiplicar por NOT(x5)
NOT(x) multiplicar por x3 multiplicar por x4 más x uno multiplicar por x multiplicar por x5 más x3 multiplicar por x1 multiplicar por NOT(x4) multiplicar por NOT(x1) más x2 multiplicar por x4 más NOT(x2) multiplicar por NOT(x3) multiplicar por x4 más x2 multiplicar por x4 más (x1 multiplicar por x multiplicar por x3 más 1) multiplicar por (NOT(x1) multiplicar por NOT(x3) más NOT(x1) multiplicar por x3 multiplicar por x4 más NOT(x1) multiplicar por x3 multiplicar por NOT(x4) más NOT(x1) multiplicar por NOT(x3)) más NOT(x1 multiplicar por x2) más x1 multiplicar por x2 multiplicar por NOT(x5)
NOT(x)x3x4+x1xx5+x3x1NOT(x4)NOT(x1)+x2x4+NOT(x2)NOT(x3)x4+x2x4+(x1xx3+1)(NOT(x1)NOT(x3)+NOT(x1)x3x4+NOT(x1)x3NOT(x4)+NOT(x1)NOT(x3))+NOT(x1x2)+x1x2NOT(x5)
NOTxx3x4+x1xx5+x3x1NOTx4NOTx1+x2x4+NOTx2NOTx3x4+x2x4+x1xx3+1NOTx1NOTx3+NOTx1x3x4+NOTx1x3NOTx4+NOTx1NOTx3+NOTx1x2+x1x2NOTx5
Expresiones semejantes
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4-x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)-x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3-1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4-NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)-x1*x2*NOT(x5)
NOT(x)*x3*x4-x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)-NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))-NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5-x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4-(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4-NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)
NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)-NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)

Lógica matemática/ NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)

Expresión NOT(x)x3x4+x1xx5+x3x1NOT(x4)NOT(x1)+x2x4+NOT(x2)NOT(x3)x4+x2x4+(x1x*x3+1)(NOT(x1)NOT(x3)+NOT(x1)x3x4+NOT(x1)x3NOT(x4)+NOT(x1)NOT(x3))+NOT(x1x2)+x1x2NOT(x5)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

Solución

Ha introducido [src]

(x2∧x4)∨(x∧x1∧x5)∨(¬(x1∧x2))∨((¬x1)∧(¬x3))∨(x1∧x2∧(¬x5))∨(x3∧x4∧(¬x))∨(x3∧x4∧(¬x1))∨(x3∧(¬x1)∧(¬x4))∨(x4∧(¬x2)∧(¬x3))∨(x1∧x3∧(¬x1)∧(¬x4))

$$\left(x_{2} \wedge x_{4}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x \wedge x_{1} \wedge x_{5}\right) \vee \left(x_{1} \wedge x_{2} \wedge \neg x_{5}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \neg \left(x_{1} \wedge x_{2}\right)$$

Solución detallada

$$\neg \left(x_{1} \wedge x_{2}\right) = \neg x_{1} \vee \neg x_{2}$$
$$x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4} = \text{False}$$
$$\left(x_{2} \wedge x_{4}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x \wedge x_{1} \wedge x_{5}\right) \vee \left(x_{1} \wedge x_{2} \wedge \neg x_{5}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \neg \left(x_{1} \wedge x_{2}\right) = x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$

Simplificación [src]

$$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$

x∨x4∨(¬x1)∨(¬x2)∨(¬x5)

Tabla de verdad

+---+----+----+----+----+----+--------+
| x | x1 | x2 | x3 | x4 | x5 | result |
+===+====+====+====+====+====+========+
| 0 | 0  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 0  | 1  | 0      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 0  | 1  | 0      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+

FND [src]

Ya está reducido a FND

$$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$

x∨x4∨(¬x1)∨(¬x2)∨(¬x5)

FNDP [src]

$$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$

x∨x4∨(¬x1)∨(¬x2)∨(¬x5)

FNCD [src]

$$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$

x∨x4∨(¬x1)∨(¬x2)∨(¬x5)

FNC [src]

Ya está reducido a FNC

$$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$

x∨x4∨(¬x1)∨(¬x2)∨(¬x5)