Conceptos Básicos de Teoría de Conjuntos: Cuestionarios y Ejercicios

Question 1

Consider the sets A and B defined as follows:
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
What is the intersection of sets A and B?

Accepted Answer

{3, 4}

Answer

{1, 2}

Answer

{5, 6}

Answer

{1, 2, 3, 4, 5, 6}

Question 2

Consider the sets A and B defined as follows:
A = {1, 2, 3, 4}
B = {5, 6, 7, 8}
Which of the following operations results in the set {1, 2, 3, 4, 5, 6, 7, 8}?

Accepted Answer

A ∪ B

Answer

A - B

Answer

A ∩ B

Answer

B - A

Question 3

Which of the following Venn diagrams correctly represents the sets A = {1, 2, 3, 4} and B = {3, 4, 5, 6}?

Accepted Answer

[Image of a Venn diagram with two overlapping circles labeled 'A' and 'B', containing the elements 3 and 4 in the overlap]

Answer

[Image of a Venn diagram with two non-overlapping circles labeled 'A' and 'B']

Question 4

Consider the set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and the set A = {2, 4, 6, 8}. What is the complement of set A with respect to U?

Accepted Answer

{1, 3, 5, 7, 9, 10}

Answer

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Answer

{2, 4, 6, 8}

Answer

{2, 4, 6, 8, 11}

Question 5

Which of the following is a valid power set of the set {a}?

Accepted Answer

{ ∅, {a} }

Answer

{ {a}, {b} }

Answer

{ a, {a} }

Answer

{ ∅, {}, {a} }

Question 6

Which of the following is NOT a property of equivalence relations?

Accepted Answer

Asymmetric

Answer

Reflexive

Answer

Transitive

Answer

Symmetric

Question 7

Consider the relation R = { (1, 2), (2, 3), (3, 1) }. Is relation R transitive?

Accepted Answer

No

Answer

Yes

Answer

Cannot be determined

Answer

Only if 3 is related to 2

Question 8

¿Qué símbolo matemático representa la relación de subconjunto?

Accepted Answer

⊂

Answer

∩

Answer

∪

Answer

∈

Question 9

Sean los conjuntos A = {1, 2, 3} y B = {2, 3, 4}. ¿Cuál es el resultado de la intersección A ∩ B?

Accepted Answer

{2, 3}

Answer

{1, 4}

Answer

{1, 2, 3}

Answer

{2, 3, 4}

Question 10

En la teoría de conjuntos, ¿cómo se define el complemento de un conjunto A en el universo U?

Accepted Answer

U - A

Answer

A ∪ U

Answer

A - U

Answer

A ∩ U

Question 11

Sean los conjuntos A = {x | x es un número par} y B = {x | x es un múltiplo de 3}. ¿Cuál es el resultado de la intersección A ∩ B?

Accepted Answer

{6}

Answer

{2, 3, 6}

Answer

{1, 2, 3}

Answer

{0, 3, 6}

Question 12

¿Cuántos elementos tiene el conjunto potencia de un conjunto con n elementos?

Accepted Answer

2^n

Answer

n + 1

Answer

n - 1

Answer

n^2

Question 13

Sean los conjuntos A = {a, e, i, o, u} y B = {b, c, d, f, g}. ¿Cuál es el resultado de la unión A ∪ B?

Accepted Answer

Conjunto con todas las letras del alfabeto

Answer

Conjunto con todas las vocales

Answer

Conjunto vacío

Answer

Conjunto con todas las consonantes

Question 14

¿Cuál de los siguientes conjuntos es un subconjunto propio del conjunto A = {1, 2, 3, 4, 5}?

Accepted Answer

B = {2, 4}

Answer

C = {1, 3, 5, 7}

Answer

D = {6, 7, 8}

Answer

E = {1, 2, 3, 4, 5}

Question 15

Dados los conjuntos A = {1, 2, 3} y B = {3, 4, 5}, ¿cuál es su unión?

Accepted Answer

C = {1, 2, 3, 4, 5}

Answer

E = {3}

Answer

D = {1, 2, 3, 3, 4, 5}

Question 16

Sean los conjuntos A = {1, 2, 3, 4} y B = {3, 4, 5, 6}. ¿Cuál es su intersección?

Accepted Answer

C = {3, 4}

Answer

E = {1, 2, 3, 4, 5, 6}

Answer

D = {1, 2}

Question 17

Considerando el conjunto universal U = {1, 2, 3, 4, 5, 6}, ¿cuál es el complemento del conjunto A = {1, 3, 5}?

Accepted Answer

B = {2, 4, 6}

Answer

D = {4}

Answer

C = {1, 3, 5}

Answer

E = {∅}

Question 18

¿Qué diagrama de Venn representa correctamente la intersección de los conjuntos A y B?

Accepted Answer

Dos círculos con una región central superpuesta, representando los elementos comunes.

Answer

Dos círculos completamente separados sin elementos comunes.

Answer

Un círculo completamente contenido dentro de otro círculo.

Question 19

De las siguientes afirmaciones, ¿cuál se cumple siempre para cualquier par de conjuntos A y B?

Accepted Answer

A ∪ (B ∩ A) = A

Answer

A ∪ (B ∪ A) = B

Answer

A ∩ (B ∪ A) = B

Question 20

¿Qué conjunto representa correctamente todos los números pares menores que 10?

Accepted Answer

{2, 4, 6, 8}

Answer

{0, 2, 4, 6, 8, 10}

Answer

{1, 3, 5, 7, 9}

Answer

{2, 4, 6, 8, ...}

Question 21

Dado el conjunto A = {a, b, c, d, e, f}, ¿cuál es su cardinalidad?

Accepted Answer

6

Answer

Infinita

Answer

5

Answer

7

Question 22

Determine el conjunto potencia del conjunto A = {1, 2}.

Accepted Answer

{{}, {1}, {2}, {1, 2}}

Answer

{{1}, {2}, {1, 2}}

Answer

Answer

{{}, {1}, {2}}