Unidad#1. Examen Final. Teoria Y Operaciones De Conjuntos.

1. EL CONJUNTO UNIVERSAL ES EL QUE CONTIENE A TODOS LOS ELEMENTOS

verdadero

falso

The given statement is true. The universal set is the set that contains all the elements. In other words, it includes every possible element that can be considered in a particular context or problem.

Explanation

The given statement is true. The universal set is the set that contains all the elements. In other words, it includes every possible element that can be considered in a particular context or problem.

2. LA INTERSECCION DE LOS CONJUNTOS ES:

2, 3

3

{ }

The correct answer is an empty set. This is because the given sets have no common elements, so their intersection is empty.

Explanation

The correct answer is an empty set. This is because the given sets have no common elements, so their intersection is empty.

3. LA PARTE SOMBREADA REPRESENTA LA OPRACION A ∩ B ∩ C

verdadero

falso

The shaded part represents the intersection of sets A, B, and C. This means that the shaded area represents the elements that are common to all three sets. Therefore, the statement is true.

Explanation

The shaded part represents the intersection of sets A, B, and C. This means that the shaded area represents the elements that are common to all three sets. Therefore, the statement is true.

4. SIMBOLOS QUE REPRESENTAN UN CONJUNTO

unitario

vacio

complemento

The correct answer is "vacio," which means "empty" in English. In the context of symbols representing a set, "vacio" refers to the symbol that represents an empty set, a set with no elements. This symbol is often denoted as Ø or {}.

Explanation

The correct answer is "vacio," which means "empty" in English. In the context of symbols representing a set, "vacio" refers to the symbol that represents an empty set, a set with no elements. This symbol is often denoted as Ø or {}.

5. PARA HALLAR EL CONJUNTO POTENCIA P(A), SE DEBEN ESCRIBIR ENTRE LLAVES TODOS LOS SUBCONJUNTOS DEL CONJUNTO

verdadero

falso

The given statement is true. In order to find the power set of a set A, all the subsets of the set should be written within curly braces. The power set of a set is the set of all possible subsets of that set, including the empty set and the set itself. Therefore, the correct answer is true.

Explanation

The given statement is true. In order to find the power set of a set A, all the subsets of the set should be written within curly braces. The power set of a set is the set of all possible subsets of that set, including the empty set and the set itself. Therefore, the correct answer is true.

6. LOS CONJUNTOS SIGUIENTES SE DICE QUE SON DISJUNTOS:

verdadero

falso

Los conjuntos se dicen que son disjuntos cuando no tienen elementos en común, es decir, no comparten ningún elemento. Por lo tanto, la afirmación de que los conjuntos siguientes son disjuntos es verdadera, ya que no se mencionan los conjuntos específicos y se asume que no tienen elementos en común.

Explanation

Los conjuntos se dicen que son disjuntos cuando no tienen elementos en común, es decir, no comparten ningún elemento. Por lo tanto, la afirmación de que los conjuntos siguientes son disjuntos es verdadera, ya que no se mencionan los conjuntos específicos y se asume que no tienen elementos en común.

7. LA EXPRESION SIGUIENTE SE UTILIZA PARA DETERMINAR:

la unión de dos conjuntos

la interseccion de conjuntos

el número de subconjuntos

La expresión se utiliza para determinar el número de subconjuntos.

Explanation

La expresión se utiliza para determinar el número de subconjuntos.

8. REPRESENTA LA OPERACION

union

interseccion

diferencia

diferencia simétrica

The correct answer is "diferencia" because it represents the operation of finding the elements that are present in one set but not in another. In other words, it calculates the difference between two sets by removing the common elements and keeping only the unique elements from the first set.

Explanation

The correct answer is "diferencia" because it represents the operation of finding the elements that are present in one set but not in another. In other words, it calculates the difference between two sets by removing the common elements and keeping only the unique elements from the first set.

9. DOS CONJUNTOS SON EQUIVALENTES SI TIENEN LA MISMA CARDINALIDAD

verdadero

falso

Two sets are considered equivalent if they have the same cardinality, meaning they have the same number of elements. In other words, if the number of elements in both sets is equal, then the sets are equivalent. This statement is true.

Explanation

Two sets are considered equivalent if they have the same cardinality, meaning they have the same number of elements. In other words, if the number of elements in both sets is equal, then the sets are equivalent. This statement is true.

10. REPRESENTA LA OPERACION UNION

verdadero

falso

The correct answer is "falso" because the phrase "REPRESENTA LA OPERACION UNION" translates to "represents the union operation" in English. The union operation is a mathematical operation that combines two sets to form a new set containing all the elements from both sets. Since the phrase is asking if it represents the union operation, the correct answer would be "falso" (false) if it does not represent the union operation.

Explanation

The correct answer is "falso" because the phrase "REPRESENTA LA OPERACION UNION" translates to "represents the union operation" in English. The union operation is a mathematical operation that combines two sets to form a new set containing all the elements from both sets. Since the phrase is asking if it represents the union operation, the correct answer would be "falso" (false) if it does not represent the union operation.

11. LOS CONJUNTOS SE PUEDEN REPRESENTAR POR:

EXTENSION Y COMPRENSION

EXTENSION Y DIAGRAMA DE VENN

COMPRENSION Y DIAGRAMA DE VENN

EXTENSION, COMPRENSION Y DIAGRAMA DE VENN

Los conjuntos pueden ser representados de diferentes maneras, pero las tres formas más comunes son mediante la extensión, la comprensión y el diagrama de Venn.

La representación por extensión consiste en listar todos los elementos del conjunto de manera explícita. Por ejemplo, si tenemos el conjunto de los números pares menores que 10, la representación por extensión sería {2, 4, 6, 8}.

La representación por comprensión consiste en describir las características que deben cumplir los elementos del conjunto. Por ejemplo, si tenemos el conjunto de los números pares, la representación por comprensión sería {x | x es un número par}.

El diagrama de Venn es una representación gráfica que utiliza círculos para mostrar la relación entre conjuntos. Cada círculo representa un conjunto y la intersección de los círculos muestra los elementos que pertenecen a ambos conjuntos.

Por lo tanto, la respuesta correcta es que los conjuntos se pueden representar mediante la extensión, la comprensión y el diagrama de Venn.

Explanation

Los conjuntos pueden ser representados de diferentes maneras, pero las tres formas más comunes son mediante la extensión, la comprensión y el diagrama de Venn.

La representación por extensión consiste en listar todos los elementos del conjunto de manera explícita. Por ejemplo, si tenemos el conjunto de los números pares menores que 10, la representación por extensión sería {2, 4, 6, 8}.

La representación por comprensión consiste en describir las características que deben cumplir los elementos del conjunto. Por ejemplo, si tenemos el conjunto de los números pares, la representación por comprensión sería {x | x es un número par}.

El diagrama de Venn es una representación gráfica que utiliza círculos para mostrar la relación entre conjuntos. Cada círculo representa un conjunto y la intersección de los círculos muestra los elementos que pertenecen a ambos conjuntos.

Por lo tanto, la respuesta correcta es que los conjuntos se pueden representar mediante la extensión, la comprensión y el diagrama de Venn.

12. ¿Cuando un conjunto esta determinado por extensiòn?

Cuando se tiene una característica de todos sus elementos

Cuando se conoce a cada uno de sus elementos

Cuando un conjunto está determinado por extensión significa que se conoce a cada uno de sus elementos. En otras palabras, se tiene información específica sobre cada elemento que pertenece al conjunto. Esto contrasta con la determinación por comprensión, donde se describe una característica que deben cumplir los elementos del conjunto, en lugar de conocerlos individualmente. En este caso, la respuesta indica que la determinación se realiza mediante el conocimiento de cada elemento del conjunto.

Explanation

Cuando un conjunto está determinado por extensión significa que se conoce a cada uno de sus elementos. En otras palabras, se tiene información específica sobre cada elemento que pertenece al conjunto. Esto contrasta con la determinación por comprensión, donde se describe una característica que deben cumplir los elementos del conjunto, en lugar de conocerlos individualmente. En este caso, la respuesta indica que la determinación se realiza mediante el conocimiento de cada elemento del conjunto.

13. LA UNION DE LOS SIGUIENTES CONJUNTOS ESTA DADA POR

1, 2, 3, 4, 5, 6, 7, 7, 8, 9

1, 2, 3, 4, 5, 6, 7, 8, 9

5,6,7

The correct answer is the union of all the given sets, which includes all the unique elements from each set. In this case, the union of the sets 1, 2, 3, 4, 5, 6, 7, 7, 8, 9 and 1, 2, 3, 4, 5, 6, 7, 8, 9 and 5, 6, 7 is 1, 2, 3, 4, 5, 6, 7, 8, 9.

Explanation

The correct answer is the union of all the given sets, which includes all the unique elements from each set. In this case, the union of the sets 1, 2, 3, 4, 5, 6, 7, 7, 8, 9 and 1, 2, 3, 4, 5, 6, 7, 8, 9 and 5, 6, 7 is 1, 2, 3, 4, 5, 6, 7, 8, 9.

14. SIGNIFICA

elementos que estan en A

elementos que no estan en A

ambas opciones son correctas

The correct answer is "elementos que no estan en A" which means "elements that are not in A" in English. This suggests that the term "SIGNIFICA" refers to the elements that are not present in set A.

Explanation

The correct answer is "elementos que no estan en A" which means "elements that are not in A" in English. This suggests that the term "SIGNIFICA" refers to the elements that are not present in set A.

15. REPRESENTA LA OPERACION

unión

intersección

diferencia de

diferencia simétrica

The correct answer is "diferencia simétrica". This term refers to the operation of finding the elements that are present in either of the two sets, but not in both. In other words, it is the set of elements that are unique to each set.

Explanation

The correct answer is "diferencia simétrica". This term refers to the operation of finding the elements that are present in either of the two sets, but not in both. In other words, it is the set of elements that are unique to each set.

16. LOS CONJUNTOS SIGUIENTES SON:

DISJUNTOS

EQUIVALENTES

IGUALES Y EQUIVALENTES

NINGUNA DE LAS ANTERIORES

The answer "IGUALES Y EQUIVALENTES" suggests that the given sets are both equal and equivalent. This means that the sets have the same elements and also have the same properties or characteristics. In other words, they are identical in terms of their contents and their properties.

Explanation

The answer "IGUALES Y EQUIVALENTES" suggests that the given sets are both equal and equivalent. This means that the sets have the same elements and also have the same properties or characteristics. In other words, they are identical in terms of their contents and their properties.

17. EL CONJUNTO SIGUIENTE ESTA EXPRESADO POR COMPRENSION.

verdadero

falso

The given statement suggests that the following set is expressed by comprehension. However, the correct answer is false. This means that the set is not expressed by comprehension.

Explanation

The given statement suggests that the following set is expressed by comprehension. However, the correct answer is false. This means that the set is not expressed by comprehension.

18. EL SIMBOLO SIGNIFICA SUBCONJUNTO PROPIO

verdadero

falso

The symbol "⊂" in mathematics represents a proper subset, which means that all the elements of one set are also elements of another set, but the two sets are not equal. Therefore, the correct answer is "verdadero" (true), as the symbol signifies a proper subset.

Explanation

The symbol "⊂" in mathematics represents a proper subset, which means that all the elements of one set are also elements of another set, but the two sets are not equal. Therefore, the correct answer is "verdadero" (true), as the symbol signifies a proper subset.

19. ¿Cuando un conjunto está determinado por comprension?

Cuando se conoce algunos de sus elementos

Cuando se tiene una característica de sus elelementos

Cuando se tiene una característica común de todos sus elementos

A set is determined by comprehension when it is defined by a common characteristic or property that all its elements possess. This means that the set is formed by selecting elements that share a certain trait or feature. By having this common characteristic, it allows us to identify and determine which elements belong to the set and which do not.

Explanation

A set is determined by comprehension when it is defined by a common characteristic or property that all its elements possess. This means that the set is formed by selecting elements that share a certain trait or feature. By having this common characteristic, it allows us to identify and determine which elements belong to the set and which do not.

20. EN LA EXPRESION SIGUIENTE, LA (n) REPRESENTA:

la cardinalidad del conjunto

el nombre del conjunto

se multiplica el 2 por la n.

The expression is asking for the meaning of the variable (n) in the given context. The correct answer is "la cardinalidad del conjunto," which means that (n) represents the cardinality or the number of elements in the set. This implies that (n) is used to determine the size or quantity of the elements in the set.

Explanation

The expression is asking for the meaning of the variable (n) in the given context. The correct answer is "la cardinalidad del conjunto," which means that (n) represents the cardinality or the number of elements in the set. This implies that (n) is used to determine the size or quantity of the elements in the set.

21. EL CONJUNTO SIGUIENTE ES UNITARIO

verdadero

falso

not-available-via-ai

Explanation

not-available-via-ai

22. EN EL DIAGRAMA, EL COMPLEMENTO DE A, ES:

11, 12, 13, 14, 15, 16, 19, 20 y 21.

14, 15, 16, 19, 20, 21.

11, 12, 13, 17, 18

The correct answer is 11, 12, 13, 14, 15, 16, 19, 20 y 21. This is because the complement of set A refers to all the elements that are not present in set A. In this case, set A includes the numbers 11, 12, 13, 14, 15, 16, 19, 20, and 21. Therefore, the complement of set A would be all the numbers that are not in this list, which is 11, 12, 13, 14, 15, 16, 19, 20, and 21.

Explanation

The correct answer is 11, 12, 13, 14, 15, 16, 19, 20 y 21. This is because the complement of set A refers to all the elements that are not present in set A. In this case, set A includes the numbers 11, 12, 13, 14, 15, 16, 19, 20, and 21. Therefore, the complement of set A would be all the numbers that are not in this list, which is 11, 12, 13, 14, 15, 16, 19, 20, and 21.

23. EN EL DIAGRAMA EL COMPLEMENTO DE A U B, ES

14, 15, 16, 19, 20, 21

14. 15, 18

11, 12, 13, 17, 18

The correct answer is the set of numbers that are not present in either set A or set B. In this case, the numbers 14, 15, 16, 19, 20, and 21 are not present in either set A or set B, so they are the complement of A U B.

Explanation

The correct answer is the set of numbers that are not present in either set A or set B. In this case, the numbers 14, 15, 16, 19, 20, and 21 are not present in either set A or set B, so they are the complement of A U B.

24. ¿Qué elementos tiene el conjunto Unión "AUB" ?

Todos los elementos de A y/o los elementos de B, sin repetir.

Solo los elementos de A.

Los elementos de A y los elementos de B.

El conjunto Unión "AUB" está compuesto por todos los elementos que pertenecen a A y/o a B, sin repetir ninguno de ellos. Esto significa que si un elemento está en A, en B o en ambos conjuntos, estará presente en la Unión "AUB".

Explanation

El conjunto Unión "AUB" está compuesto por todos los elementos que pertenecen a A y/o a B, sin repetir ninguno de ellos. Esto significa que si un elemento está en A, en B o en ambos conjuntos, estará presente en la Unión "AUB".

25. EL CONJUNTO VACIO ES SUBCONJUNTO DE TODOS LOS CONJUNTOS.

verdadero

falso

The statement is true because the empty set is a subset of every set. This means that every element in the empty set is also an element of any other set. Since there are no elements in the empty set, it satisfies the condition of being a subset of all sets. Therefore, the statement is true.

Explanation

The statement is true because the empty set is a subset of every set. This means that every element in the empty set is also an element of any other set. Since there are no elements in the empty set, it satisfies the condition of being a subset of all sets. Therefore, the statement is true.

26. EL SIMBOLO SIGNIFICA DIFERENCIA DE CONJUNTOS

verdadero

falso

The given statement is false. The symbol used here, which is not specified in the question, does not represent a difference between sets. Therefore, the correct answer is false.

Explanation

The given statement is false. The symbol used here, which is not specified in the question, does not represent a difference between sets. Therefore, the correct answer is false.

27. EL CONJUNTO Q ES FINITO.

verdadero

falso

The given statement "EL CONJUNTO Q ES FINITO" translates to "The set Q is finite" in English. The correct answer is "falso" which means "false" in English. This means that the statement is incorrect and the set Q is not finite.

Explanation

The given statement "EL CONJUNTO Q ES FINITO" translates to "The set Q is finite" in English. The correct answer is "falso" which means "false" in English. This means that the statement is incorrect and the set Q is not finite.

28. EL DIAGRAMA SIGNIFICA

A ⊆ B

B ⊆ A

A ⊂ B

B ⊂ A

The given diagram represents a relationship between two elements, A and B. The notation "⊆" represents a subset relationship, meaning that A is a subset of B. Therefore, the correct answer is B ⊂ A, indicating that B is a subset of A.

Explanation

The given diagram represents a relationship between two elements, A and B. The notation "⊆" represents a subset relationship, meaning that A is a subset of B. Therefore, the correct answer is B ⊂ A, indicating that B is a subset of A.

29. EL SIGUIENTE CONJUNTO TIENE CARDINALIDAD

7

6

4

The given set has a cardinality of 6. This means that there are 6 elements in the set.

Explanation

The given set has a cardinality of 6. This means that there are 6 elements in the set.

30. Sí n(A) = 0 entonces [P(A)] = 0

verdadero

falso

If the probability of event A is zero, it means that event A cannot occur. Therefore, the probability of event A, denoted as P(A), will also be zero. In this case, the statement "Sí n(A) = 0 entonces [P(A)] = 0" translates to "If the number of elements in set A is zero, then the probability of event A is zero." This statement is false because even if the number of elements in set A is zero, the probability of event A can still be non-zero if there are other events that can occur.

Explanation

If the probability of event A is zero, it means that event A cannot occur. Therefore, the probability of event A, denoted as P(A), will also be zero. In this case, the statement "Sí n(A) = 0 entonces [P(A)] = 0" translates to "If the number of elements in set A is zero, then the probability of event A is zero." This statement is false because even if the number of elements in set A is zero, the probability of event A can still be non-zero if there are other events that can occur.

31. EL SIGUIENTE CONJUNTO TIENE UN TOTAL DE SUBCONJUNTOS IGUAL A:

3

6

8

The given set has a total of 8 subsets. To find the number of subsets, we can use the formula 2^n, where n is the number of elements in the set. In this case, the set has 3 elements, so the number of subsets is 2^3 = 8.

Explanation

The given set has a total of 8 subsets. To find the number of subsets, we can use the formula 2^n, where n is the number of elements in the set. In this case, the set has 3 elements, so the number of subsets is 2^3 = 8.

32. Considera el conjunto A={x/x ∈ N, -5 < x < 8}. Razona ¿Cuales afirmaciones son verdaderas?

-3 ∈ A

1 ∈ A

0 ∈ A

6 ∈ A

5 ∈ A

8 ∈ A

The set A is defined as the set of natural numbers x such that -5
The statement "1 ∈ A" is true because 1 is a natural number and it satisfies the condition -5
The statement "6 ∈ A" is true because 6 is a natural number and it satisfies the condition -5
The statement "5 ∈ A" is true because 5 is a natural number and it satisfies the condition -5
Therefore, the correct statements are 1 ∈ A, 6 ∈ A, and 5 ∈ A.

Explanation

The set A is defined as the set of natural numbers x such that -5
The statement "1 ∈ A" is true because 1 is a natural number and it satisfies the condition -5
The statement "6 ∈ A" is true because 6 is a natural number and it satisfies the condition -5
The statement "5 ∈ A" is true because 5 is a natural number and it satisfies the condition -5
Therefore, the correct statements are 1 ∈ A, 6 ∈ A, and 5 ∈ A.

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33. SELECCIONA LAS CUALIDADES QUE POSEE LA PALABRA CONJUNTO.

se nombra con letra mayúscula

agrupa elementos

sus elementos se agrupan entre llaves

sus elementos se separan con guiones

agrupa elementos con una caracteristica común

si sus elementos son letra, estas deberán ser minúsculas

sus elementos se separan por coma.

The correct answer is a combination of qualities that the word "conjunto" possesses. It is named with a capital letter, its elements are grouped between braces, it groups elements with a common characteristic, if its elements are letters, they should be lowercase, and its elements are separated by commas.

Explanation

The correct answer is a combination of qualities that the word "conjunto" possesses. It is named with a capital letter, its elements are grouped between braces, it groups elements with a common characteristic, if its elements are letters, they should be lowercase, and its elements are separated by commas.

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