Which of these is not a type of relation?

The correct option is Surjective.

In mathematics, specifically in set theory, a relation on a set is a collection of ordered pairs that describes a relationship between elements of the set. Binary relations are commonly classified based on specific properties. The three fundamental types of relations are:
1. Reflexive Relation: A relation $R$ on a set $A$ is reflexive if every element is related to itself, meaning for all $a\in A$, the pair $(a,a)\in R$.
2. Symmetric Relation: A relation $R$ is symmetric if for any elements $a,b\in A$, whenever $(a,b)\in R$, it must also be true that $(b,a)\in R$.
3. Transitive Relation: A relation $R$ is transitive if for any elements $a,b,c\in A$, whenever $(a,b)\in R$ and $(b,c)\in R$, it must also be true that $(a,c)\in R$.

In contrast, Surjective (also known as "onto") is a property used to describe a function (mapping), not a type of binary relation on a set. A function $f:X\to Y$ is surjective if every element in the codomain $Y$ has at least one corresponding pre-image in the domain $X$. Therefore, "Surjective" is not a type of relation.