types of relation on se sets one by one define
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Explanation:
Types of Relations
Reflexive Relation: A relation R on set A is said to be a reflexive if (a, a) ∈ R for every a ∈ A. ...
Irreflexive Relation: A relation R on set A is said to be irreflexive if (a, a) ∉ R for every a ∈ A. ...
Symmetric Relation: A relation R on set A is said to be symmetric iff (a, b) ∈ R ⟺ (b, a) ∈ R.
Answer:
Types of Relation:
Empty Relation: A relation R on a set A is called Empty if the set A is empty set.
Full Relation: A binary relation R on a set A and B is called full if AXB.
Reflexive Relation: A relation R on a set A is called reflexive if (a,a) € R holds for every element a € A .i.e. if set A = {a,b} then R = {(a,a), (b,b)} is reflexive relation.
Irreflexive relation : A relation R on a set A is called reflexive if no (a,a) € R holds for every element a € A.i.e. if set A = {a,b} then R = {(a,b), (b,a)} is irreflexive relation.
Symmetric Relation: A relation R on a set A is called symmetric if (b,a) € R holds when (a,b) € R.i.e. The relation R={(4,5),(5,4),(6,5),(5,6)} on set A={4,5,6} is symmetric.
AntiSymmetric Relation: A relation R on a set A is called antisymmetric if (a,b)€ R and (b,a) € R then a = b is called antisymmetric.i.e. The relation R = {(a,b)→ R|a ≤ b} is anti-symmetric since a ≤ b and b ≤ a implies a = b.
Transitive Relation: A relation R on a set A is called transitive if (a,b) € R and (b,c) € R then (a,c) € R for all a,b,c € A.i.e. Relation R={(1,2),(2,3),(1,3)} on set A={1,2,3} is transitive.
Equivalence Relation: A relation is an Equivalence Relation if it is reflexive, symmetric, and transitive. i.e. relation R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)} on set A={1,2,3} is equivalence relation as it is reflexive, symmetric, and transitive.
Asymmetric relation: Asymmetric relation is opposite of symmetric relation. A relation R on a set A is called asymmetric if no (b,a) € R when (a,b) € R.
Explanation:
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