What is the difference between reflexive and transitive

Certainly it is symmetric and transitive, but it is not reflexive, as a guy without a job isn't related to himself.

In particular, reflexivity holds in all points in relation with something other. There are many examples of this:. PERs can be used to simultaneously quotient a set and imbue the quotiented set with a notion of equivalence.

A genuinely useful example copied straight from the linked page is functions that respect equivalence relations of the domain and codomain. This is true even if equality of functions in the underlying set theory is more intensional — hence the use of this technique in type theory. I had the same question as you did but as soon as I read yours I noticed where the confusion came from: it lied in the if and only if part of the definition of symmetry. This doesn't necessarily mean the relation is not symmetric, it only means you can't prove it using the given facts.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Example of a relation that is symmetric and transitive, but not reflexive [duplicate] Ask Question. Recall congruence means two objects are physically identical. In the world of geometry, they have the same shape and size. Reflexive Think of an object--it can be an object you see on your desk, in your room; or it can be a geometric figure: a square, a triangle, etc.

Is this object congruent to itself? Is a mug physically identical to itself? Does a triangle have the same shape and size as itself? The answer is yes to all these questions. A geometric figure is always congruent to itself.

This means congruence is reflexive. Symmetric Now imagine the following scenario. You recently saw your friend wearing a pair of awesome sneakers. You then went online and found the same pair of sneakers and purchased it. The pair of new sneakers you got are, evidently, identical--or congruent to your friend's sneakers. Nonetheless, it is possible for a relation to be neither reflexive nor irreflexive.

Many students find the concept of symmetry and antisymmetry confusing. Even though the name may suggest so, antisymmetry is not the opposite of symmetry.

It is possible for a relation to be both symmetric and antisymmetric, and it is also possible for a relation to be both non-symmetric and non-antisymmetric. It is clearly irreflexive, hence not reflexive.

Thus the relation is symmetric. Likewise, it is antisymmetric and transitive. It is clearly reflexive, hence not irreflexive. It is also trivial that it is symmetric and transitive. It is reflexive hence not irreflexive , symmetric, antisymmetric, and transitive.

Here are two examples from geometry.