Types of set relations in mathematics | Domain, range of the relation

Know about different types of relations in the set of mathematics . Defined with examples. Also, know the domain and range of the relation. ...

Know about different types of relations in the set of mathematics. Defined with examples. Also, know the domain and range of the relation.

Types of set relations in mathematics

1. One to many relation
2. Many to one relation
3. One to one relation

One to many relation

Let, two sets are A and B. In the A set there are some students, and in the B set, there are some courses. In the Ven diagram, we can see, one student has taken multiple numbers of courses. Both can be represented as pairs of sets.

This is one to many relation.

Every element of set A is related to multiple elements of set B. Because one student can take multiple courses.

Many to one relation

Let set A is set of some students and set B is the set of the rooms of students. In a single room, multiple students can live. In the Ven diagram we see, multiple students got one room. So, multiple elements of set A are related to set B.

This is many to one relation.

One to one relation

If two sets A, B are not empty then the cross product of A and B or the subset of the cross product is called a relation from A to B.

Set A is the ID of some students and B set is the names of those students. In the Ven diagram, we see one student has only one ID. 

This is one to one relation.

Let R is a relation from set A to set B then we can write,

R⊆ AｘB 

If a∈A  and b∈B  then we say a is related with b and write aRb.

If a∉A  and b∉B  then we say a is not related to b.

Remember: If we use ⊆ (subset or equal sign) that means the first set is the subset of the second set or both are equal.

Domain, range of the relation

If R⊆ AｘB then we know R is said a relation from set A to set B

Here, 

Domain of R is = {a:(a,b)∈R}

Range of R = {b:(a,b)∈R }