Types of Relations A relation is a relationship between two sets of elements. There are two main types of relations: reflexive and non-reflexive. Reflexiv...
Types of Relations
A relation is a relationship between two sets of elements. There are two main types of relations: reflexive and non-reflexive.
Reflexive Relations
A relation is reflexive if every element in the set is related to itself. For example, the relation "is sibling to" on the set of people is a reflexive relation, since every person is related to themselves.
Non-reflexive Relations
A relation is non-reflexive if no element in the set is related to itself. For example, the relation "is taller than" on the set of people is a non-reflexive relation, since no person is taller than themselves.
Symmetric Relations
A relation is symmetric if the relation is reflexive and non-reflexive at the same time. For example, the relation "is equal to" on the set of real numbers is a symmetric relation, since it is reflexive (every element is equal to itself) and it is non-reflexive (no two elements are equal to each other).
Transitive Relations
A relation is transitive if the relation is reflexive and symmetric. For example, the relation "is a parent of" on the set of people is a transitive relation, since it is reflexive (every parent is related to a child), and it is symmetric (if A is a parent of B, and B is a parent of C, then A is a parent of C).
Example
Suppose we have the set of students in a class. The relation "is taking Calculus" can be represented by the following graph:
Student 1 --> Taking Calculus
Student 2 --> Taking Calculus
Student 3 --> Taking Calculus
Student 4 --> Not Taking Calculus
Student 5 --> Not Taking Calculus
This graph shows that the relation is reflexive (every student takes Calculus at least once), non-reflexive (student 4 does not take Calculus), symmetric (if student A takes Calculus, then student B must also take Calculus), and transitive (if student A is taking Calculus, and student B is taking Calculus, then student C must also be taking Calculus)