Teoria de conjuntos

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         TEORIA DE CONJUNTOS

Profesor:                                                                      Integrantes:

Betzimar Puerta                                                                 Gabriela Verde

                                                                                   30.363.286

                                             El Tigre, mayo 2021

Dados los siguientes conjuntos, determine que conjuntos se forman según su simbología. 2

Si U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 15 }

A = { 4, 8, 10, 12 }                                                     B = { 3, 6, 9, 12, 15 }

C = { 1, 2, 3, 11, 12, 13 }                                          D = { 1, 5, 6, 10, 11 }

 E = {12, 13, 14, 15}

 a) A ∪ B={4,8,10,12,3,6,9,15}

b) (A ∩ B)c = {12}

(A ∩ B) = {12}

(A ∩ B)c = {1,2,3,4,5,6,7,8,9,10,11,13,14,15}

(A ∩ B)c= {1,2,3,4,5,6,7,8,9,10,11,13,14,15}

c) (D ∩ E) – A

D ∩ E)= {ø}

(D ∩ E)= {ø} – A={ø}

(D ∩ E)–A={ø}

d) B – C={6,9,15}

e) Ac={1,2,3,4,5,6,7,9,11,13,14,15}

f) B c={1,2,3,4,5,7,8,10,11,13,14}

g) E c ∩ D

E c={1,2,3,4,5,6,7,8,9,10,11}

E c ∩ D={1,5,6,10,11}

E c ∩ D={1,5,6,10,11}

h) B c ∆ Ec

 c={1,2,3,4,5,7,8,10,11,13,14}

E c={1,2,3,4,5,6,7,8,9,10,11}

B c ∆ Ec= B c– E c={13,14}∪ E c– B c={3,6,9}

                                      B c ∆ Ec={13,14,3,6,9}

B c ∆ Ec={13,14,3,6,9}

i) B c ∪ E c

B c={1,2,4,5,7,8,10,11,13,14}

E c={1,2,3,4,5,6,7,8,9,10,11}

B c ∪ E c={1,2,3,4,5,7,8,10,11,13,14,3,6,9}

B c ∪ E c={1,2,3,4,5,7,8,10,11,13,14,3,6,9}

j) A ∆ C= A – C ={4,8,10}∪ C-A ={1,2,3,11,13}

A ∆ C={4,8,10,1,2,3,11,13}

k) ( Bc ∪ C)c 3

B c={1,2,4,5,7,8,10,11,13,14}

( Bc ∪ C)={1,2,4,5,7,8,10,11,13,14,3,12}

( Bc ∪ C)c={6,9,15}

L) ( C ∆ D )c

( C ∆ D )=( –D={2,3,12,13}∪ D–C={5,6,10}

                                     ( C ∆ D )={2,3,12,13,5,6,10}

 ( C ∆ D )c={1,4,7,8,9,11,14,15}

 ( C ∆ D )c={1,4,7,8,9,11,14,15}

2) Si U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} es el conjunto universal y A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, C = {2, 4, 6, 8}:

a) A ∆ B=A–B={7,10}∪ B–A={2,3,5}

A ∆ B={7,10,2,3,5}

b) A-B={7,10}

c) A c={2,3,5,6,8,9}

d) U c= ø e) B ∩ U={1,2,3,4,5}

f) B C ∩ (C − A)

 (C − A)={2,6,8}

B C={6,7,8,9,10}

B C ∩ (C − A)={6,7,8,9,10,2,6,8}={6,8}

B C ∩ (C − A)={6,8}

g) (A∩B) c ∪ C

 (A∩B) c ∪ C=(A∩B)={1,4}

 (A∩B) c={2,3,5,6,7,8,9,10}

A∩B) c ∪ C={2,3,5,6,7,8,9,10,4}

h) B ∩ C={2,4}

i) A ∪ ø={1,4,7,10}

j) A ∩ (B ∆ C)

 (B ∆ C)=B−C={1,3,5}∪ C-B={6,8}

                     (B ∆ C)={1,3,5,6,8}

A ∩ (B ∆ C)={1}

k) (A ∩ B) ∆ C

(A ∩ B)={1,4}

(A ∩ B) ∆ C=(A ∩ B)−C={1}∪ C−(A ∩ B)={2,6,8}

                     (A ∩ B) ∆ C={1,2,6,8}

 (A ∩ B) ∆ C={1,2,6,8}

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