Trying to Understand the Meaning of Transitivity in Relation to a Particular Problem I was trying to understand transitive relation and so I was solving a problem. The question is : $R_1 = \{(a,b)| a =b \text{ or }a = -b\} , R_2 = \{(a,b)| a =b \}, R_3 = \{(a,b)| a =b+1\}$, which one is transitive and why?
As far as I know transitive relation is, if $a>b$ and if $b > c$, then $a> c$. I am assuming that the given a and b are real numbers but I am not sure where I will get C so that I can show that which one is transitive.
I saw many youtube tutorials and read my book but I am very confused with this math. I am new in this topic. It will be really helpful if someone can please explain how can I solve this problem. 
Thank you very much.

Relations are just collections of ordered pairs. For example, a relation on the set of real numbers $\mathbb{R}$ would be $(x,y)$ pairs. Formally, a relation on a set $S$ is simply some subset of the cartesian product $R \subseteq S \times S$. We say a relation $R$ is transitive if whenever the pairs $(a,b), (b,c) \in R$ then $(a,c) \in R$ as well. In the first relation, if we know $(a,b), (b,c) \in R_1$, then we know either $a = b$ or $a = -b$. Similarly, either $b = c$ or $b = -c$. Clearly this implies either $a = c$ or $a = -c$ as we know the magnitudes of a,b,c must be the same. Thus $(a,c) \in R_1$ and the relation is transitive.
