Name: Parte 1. Relación de pares ordenados. Producto Cartesiano.
Uploaded: 2020-03-19T01:32:35.000Z
Duration: 32 min 54 s
Description: Sean A = {4,5,6} y B = {2,4,6,12}, R1, R2 y R3 relaciones definidas así: R1 = {(x,y)/ ϵ A X B / x = y} R2 = {(x,y)/ ϵ A X B / x = y + 2} R3 = {(x,y)/ ϵ A X B/ y = 2x} * Hallar A X B= * Escribir cada relación como un conjunto de pares ordenados.

Parte 1. Relación de pares ordenados. Producto Cartesiano.

Resolving a Mathematical Exercise Involving Relations and Cartesian Products

Introduction to the Problem

The exercise involves two sets: Set A with elements 4, 5, 6 and Set B with elements 2, 4, 6, 12.

Three relations are defined between these sets: Relation 1 (x = James), Relation 2 (x = 2), and Relation 3 (y = 2x).

Cartesian Product Calculation

The first step is to calculate the Cartesian product of sets A and B.

A visual representation (diagrama sagital) is created to illustrate the mapping from set A to set B.

Each element in set A is related to multiple elements in set B:

Element 4 relates to 2, 4, 6, 12

Element 5 relates to 2, 4, 6

Element 6 relates to 2, 4, 6, 12

Forming Ordered Pairs

The ordered pairs for the Cartesian product are formed as follows:

From element 4: (4,2), (4,4), (4,6), (4,12)

From element 5: (5,2), (5,4), (5,6), (5,12)

From element 6: (6,2), (6,4), (6,6), (6,12)

Analyzing Relations

Relation One Analysis

For Relation One where x = y:

Valid pairs identified include:

Pair (4 ,4) since both values equal.

Pair (6 ,6) also satisfies this condition.

Relation Two Analysis

For Relation Two where x = y + 2:

Starting with pair (42) where x equals James plus two gives valid results.

Pair (42) works because x equals y + two; thus it’s valid.

Other pairs like (46) do not satisfy this condition.

Conclusion on Relations

Only specific pairs meet the criteria for each relation.

Further analysis shows that only certain combinations yield valid results based on their defined relationships.

Understanding Ordered Pairs and Relationships

Introduction to Ordered Pairs

The discussion begins with the introduction of two ordered pairs, specifically (4, 2) and (6, 4), which are foundational for understanding relationships in mathematics.

The speaker emphasizes the importance of identifying elements from set A that correspond to these ordered pairs.

Exploring Mathematical Relationships

The concept of a relationship defined as y = 2x is introduced. This equation will guide the search for valid ordered pairs.

The speaker examines various values for x . For instance, when x = 5 , it calculates y = 10 , leading to the ordered pair (5, 10).

Finding Valid Ordered Pairs

Continuing with the exploration, when x = 6 , it computes y = 12 , resulting in the valid ordered pair (6, 12).

The final conclusion highlights that (6, 12) is indeed part of the relationship defined earlier. The session wraps up with an invitation for viewers to subscribe and engage further.

Conclusion