Reflexive Relation
A relation is reflexive if every element is related to itself.
In other words: every element includes itself. Thus, pairs like (1,1), (2,2), (3,3), and so on are always in the relation.
Examples of Reflexive Relations
- The "=" relation is reflexive because every number equals itself (e.g., 5 = 5).
- The "≤" relation is reflexive because every number is less than or equal to itself (e.g., 7 ≤ 7).
Counterexamples (Non-Reflexive Relations)
- The "<" relation is not reflexive because a number is never less than itself.
- The divisibility relation is not reflexive if the set includes 0, since 0 does not divide itself.
Summary
The essence of a reflexive relation is that every element is related to itself. If any element is missing the (a,a) pair from the relation, it is no longer reflexive.
Practice Exercise
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