Types of relations: (1) Reflexive: (a,a) ∈ R for all a ∈ A; (2) Symmetric: If (a,b) ∈ R, then (b,a) ∈ R; (3) Transitive: If (a,b), (b,c) ∈ R, then (a,c) ∈ R; (4) Equivalence: reflexive + symmetric + transitive. Examples: Equality (=) is equivalence. Less than (<) is transitive but not reflexive/symmetric. Reflexive example: R = {(1,1), (2,2), (1,2)} on {1,2} is reflexive. Symmetric example: R = {(1,2), (2,1)} is symmetric. Testing: Check each property for relation. Equivalence relations partition set into equivalence classes. Exam tip: Distinguish relation types. Recognize modular arithmetic relations are equivalence. Practice: Proving/disproving properties.