PRÁCTICA(3:(RELACIONES(Y(ESTRUCTURAS(
1. Encuentre(el(dominio(y(el(rango(de(las(siguientes(relaciones:(
a) A={a,b,c,d}+B={1,2,3}+++R={(a,1)+(a,2)+(b,1)+(c,2)+(d,1)}+
b) A=B{1,2,3,4,8}((aRb((si(a(es(múltiplo(de(b(
+
2. Dada(A={1,2,3,4}((y(B={a,b,c}(Calcular(A×B!y!B×A.(Escribir(la(matriz(de(las(
relaciones(R1={((1,a),(3,c),(4,b),(4,c)(}(y(R2={((a,2),(b,2),(c,3),(c,4)(}((((
3. Dadas(A=
101
011
110
000
,(B=
110
101
001
110
(y(C=
100
011
101
((
Calcular(𝐴∨𝐵,𝐴∧𝐵,𝐵⨀𝐶,𝐴⨀𝐵(
+
4. Sea(A={1,2,3,4}(Defina(por(extensión(y(en(forma(de(grafo(la(relación(determinada(
por:(
1010
0010
1000
1101
(
(
En(el(grafo(correspondiente(determine(las(entradas(y(salidas(de(cada(vértice,(el(grado(
del(grafo(y(calcule(MR2(y(MR3(
(
5. Dada(la(siguiente(relación:(R={(0,0)+(0,1)+(0,3)+(1,1)+(1,0)+(2,3)+(3,3)}((
(
a) Escribir(la(matriz(de(la(relación(
b) Dibujar(el(grafo(correspondiente(
c) Determinar(y(justificar(si(es(reflexiva,(simétrica(o(transitiva.(Cuál(es(su(
cerradura(transitiva?(
d) Calcular(MR2(
(
6. En(las(siguientes(relaciones(determine(si(son(reflexivas,(irreflexivas,(simétricas,(
asimétricas,(antisimétricas(o(transitivas.(
a) R(=({(1,1)((1,2)((2,1)((2,2)((3,3)((3,4)((4,3)((4,4)}(
b) R(=({(1,3)((1,1)((3,1)((1,2)((3,3)((4,4)}(
c) (
(
d)
0101
1011
0100
1100
(
(
