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.

Try replacing, for example, your $a \gt b$ with $\{a,b\} \in R_1$, $b \gt c$ with $\{b,c\} \in R_1$ and $a \gt c$ with $\{a,c\} \in R_1$. Then replace $R_1$ with $R_2$ and $R_3$ to see for which of these the first $2$ statements (e.g., if $\{a,b\} \in R_1$ and $\{b,c\} \in R_1$) means the third one must hold as well (e.g., $\{a,c\} \in R_1$).
If you do this, you should find that $R_1$ and $R_2$ are transitive, while $R_3$ is not (because $a = b + 1$ and $b = c + 1$ means $a = c + 2$, not $a = c + 1$). Can you finish the rest yourself?
