Transitive Relations | Examples of relations that are reflexive , symmetric, transitive | 11 |

Transitive Relations | Examples of relations that are reflexive , symmetric, transitive | 11 |

1. In this lecture we will introduce the concept of Transitive relations. We shall discuss how are transitive relations different from relations.
2. 'Is a biological sibling' is a transitive relation as if one person A is a biological sibling of another person B, and B is a biological sibling of C, then A is a biological sibling of C.
3. A relation R is called intransitive if it is not transitive, that is, if xRy and yRz, but not xRz, for some x, y, z. In contrast, a relation R is called antitransitive if xRy and yRz always implies that xRz does not hold.

An intransitive relationship would be one in which such a conclusion did not necessarily follow. Such relationships appear to be illogical and inconsistent but are often found in matters of personal preference or other subjective judgments. For example, a person might prefer the color blue over red and red over green, but when given a choice, he or she might prefer green over blue.

Learning Objectives:
1. Defining Transitive relation on A
2. Defining intransitive relation on A
3. Examples checking transitivity on A
4. Examples checking all, reflexivity, symmetry and transitivity on A
5. Difference between transitive and intransitive relations


This is useful for all those students who are preparing for any entrance that would test you on the basics of Advance mathematics and calculus, specifically

1. Basics for MA Economics
2. Semester Exam, mathematical methods
3. Indian Economic Services

[harshbhardwaj]

Hi ma'am, I don't grasp why, at 20:33, the relation is symmetric when the condition doesn't hold but when at transitive it doesn't then the relation is not transitive, when in both cases there are scenarios where the condition doesn't hold. Also the logic given for it would also hold true for reflexive making it hold true for the relation. Kind request to clarify. Thank you