(a1, a2) ∈R implies that (a2, a1) ∈ R, for all a1, a2∈A. This condition is for which of the following relations?

The correct option is Symmetric relation.

In set theory, a binary relation $R$ defined on a set $A$ is a collection of ordered pairs $(x,y)$ where $x,y\in A$.

Relations are classified into different types based on specific conditions:
1. Reflexive relation: A relation $R$ on a set $A$ is reflexive if every element of $A$ is related to itself. That is, $(a,a)\in R$ for all $a\in A$.
2. Symmetric relation: A relation $R$ on a set $A$ is symmetric if whenever an element $a_1$ is related to $a_2$, then $a_2$ is also related to $a_1$. In mathematical notation, this is expressed as: if $(a_1,a_2)\in R$, then $(a_2,a_1)\in R$ for all $a_1,a_2\in A$.
3. Equivalence relation: A relation is an equivalence relation if it is reflexive, symmetric, and transitive.
4. Universal relation: A relation in which every element of set $A$ is related to every element of set $A$, i.e., $R=A\times A$.

Since the given condition states that $(a_1,a_2)\in R$ implies $(a_2,a_1)\in R$ for all $a_1,a_2\in A$, this directly matches the definition of a Symmetric relation.