In Set Theory and Discrete Mathematics, a Reflexive Relation is one of the most fundamental properties a relation can have on a set. It is a core concept in Class 12 Mathematics (Relations and Functions).
For a relation to be an 'Equivalence Relation', it must satisfy three properties simultaneously: it must be Reflexive, Symmetric, and Transitive.
A relation R on a set A is called Reflexive if every element of set A is related to itself.
Mathematically: (a, a) ∈ R for every a ∈ A.
This means if you look at the set, every single element must have a 'loop' pointing back to itself in the relation.
Let Set A = {1, 2, 3}.
Relation R₁ = {(1,1), (2,2), (3,3), (1,2)} Is it reflexive? YES. Because (1,1), (2,2), and (3,3) are all present. The extra (1,2) doesn't break the rule.
Relation R₂ = {(1,1), (2,2), (1,3)} Is it reflexive? NO. Because the element '3' is in the set A, but the pair (3,3) is missing from the relation R₂.
An irreflexive relation is the exact opposite. A relation R on set A is irreflexive if NO element is related to itself. (i.e., (a,a) ∉ R for all a ∈ A). Example: 'Is strictly less than' (<).
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