EMPTY RELATIONS - An empty relation is a type of relation, there is no relation between any object / element of sets. Empty relation is also called void relation.
Therefore, R = ΙΈ
EXAMPLE - A = Set of all student of boys school
R = {(a, b) ; a and b are sisters}.
UNIVERSAL - A relation R in a set A is called universal relation if each element of set A is related to every element of A. Universal Relation is also called full relation.
Therefore, R = A❌A.
EXAMPLE - R = {(a, b) : a and b is greater than 2 feet}.
IDENTITY - A relation R in a set A is called identity relation if every element of set A is related to itself only.
Therefore, R = I {(a,a) belongs to A}.
INVERSE - Let R be a relation from set A to set B.
Therefore R belongs to A❌B.
The relation R-1 is called inverse relation, if relation from set B to A is denoted by R-1 = {(b, a) : a and b belongs to R}.
EXAMPLE - R = {(1, 2), (2,3)}
R-1 = {(2,1), (3,2)}.
REFLEXIVE - If every element of set A maps to itself.
for every a ∈ A, (a, a) ∈ R.
SYMMETRIC - A relation R in a set A is said to be symmetric if (a,b) ∈ R then (b,a) ∈ R.
TRANSITIVE - A relation in a set A is said to be transitive, if
(a,b) ∈ R , (b, c) ∈ R , then (a, c) ∈ R.
EQUIVALENCE - A relation is said to be equivalence relation if it is reflexive, symmetric and transitive relation.
EXAMPLE - If we throw two dices A and B and note down all the possible outcome.
Define, a relation; R = {(a, b) : a ∈ R , b ∈ R}
we find that {(1,1), (2, 2), (3, 3), (4, 4),......} ∈ R (Reflexive)
If {(a,b) = (1,2) ∈ R} then {(B,A) = (2,1)} ( Symmetric)
IF {(a,b) = (1, 2) ∈ R }, {(b,c) = (2,3) ∈ R }
then {(a,c ) = (1,3) ∈ R } (Transitive ).
