# Equivalence Relations

by kingstar
Tags: equivalence, relations
 P: 38 Hi, I'm reading a book on sets and it mentions a set B = {1,2,3,4} and it says that R3 = {(x, y) : x ∈ B ∧y ∈ B} What does that mean? Does that mean every possible combination in the set? Also the book doesn't clarify this completely but for example using the set B say i had another set R = {(1,2),(2,3),(1,3),(1,1),(2,2),(3,3),(4,4)}, Would this be clarified as transitive and reflexive? My question is does a set need to have all transitive properties and all the reflexive properties to be called transitive and reflexive. If i had another set: R1 = {(1,2),(2,3),(1,3),(1,1),(2,2),(3,3)} In which i removed (4,4) would this set R1 still be considered reflexive? Thanks in advance
 Sci Advisor P: 1,810 Your first example is a transitive and reflexive relation. A relation is transitive and reflexive if it satisfies the axioms for transitivity and reflexivity. Your other example is not reflexive, since 4 is an element of X, but 4 ~ 4 is not satisfied.
Math
Emeritus