This document defines several languages and their operations. It defines the union and concatenation of languages L1 and L2. It also defines the language generated by the regular expression 0(0+1)* and provides two ways to write it - using union and concatenation. It provides four words over the alphabet {0,1}.

1. REPUBLICA BOLIVARIANA DE VENEZUELA
INTEGRANTE:
Ángel Colmenares
CI. 19.973.060
VICERRECTORADO ACADÉMICO
UNIVERSIDAD FERMIN TORO
FACULTAD DE INGENIERÍA
FACULTAD DE INGENIERIA
AUTÓMATAS

2. EJERCICIO #1
Definir los siguientes lenguajes:
 L1 U L2 = {X|X E Σ1 ó X E Σ2 }
L1 U L2 = {11,22,33,44,55,66,77,88,aa,bb,cc,dd,ee,ff,gg}
 (L1.L2)2 = {X2 = X.X|X E (L1.L2)}
(L1.L2)2 = {11aa 11aa, 11aa 22aa, 11aa 33aa, 11aa 44aa…
55cc 11aa, 55cc 22aa, 55cc 33aa, 55cc 44aa…
88bb 11aa, 88bb 22aa, 88bb 33aa, 88bb 44aa…}
 L1.L2 = {XY|X E Σ1 e Y E Σ2 }
L1.L2 = {11aa, 22aa, 33aa, 44aa, 55aa, 66aa, 77aa, 88aa,
11bb, 22bb, 33bb, 44bb, 55bb, 66bb, 77bb, 88bb,
11cc,22cc,33cc,44cc,55cc,66cc,77cc,88cc,
11dd,22dd,33dd,44dd,55dd,66dd,77dd,88dd,
11ee,22ee,33ee,44ee,55ee,66ee,77ee,88ee,
11ff,22ff,33ff,44ff,55ff,66ff,77ff,88ff,
11gg,22gg,33gg,44gg,55gg,66gg,77gg,88gg…}
EJERCICIO #2
0(0+1)*
1 .la adición
L (0(0+1)*) = L ((0+1)*
[L (0+1)]*
[L (0) + L (1)]*
[{0,1}]*
U∞
i=0 {0,1}

3. {ƛ, 0, 1, 00, 01, 10,11…}
2. concatenación
L (0(0+1)*) = [L{0}. L {ƛ, 0, 1, 00, 01, 10,11…}]
{0}. {ƛ, 0, 1, 00, 01, 10,11…}
{0}. U∞
i=0 {ƛ, 0, 1, 00, 01, 10,11…}i
{0, 00, 01, 000, 011, 010,011…}
EJERCICIO #3
Σ1 = {0, 1}
W1 (Σ)=0110
W2 (Σ)=1001
W3 (Σ)=1111
W4 (Σ)=0000