Hello,

can someone show me how to write a formal proof of equivalence relation?

I have the following problem:

Let us have a set A and a set B. Let $\displaystyle f: A \rightarrow B$. Now let us have relation R and T, where R has a relation on B and T has a relation on A with one condition, $\displaystyle (a,b) \in T$ if and only if $\displaystyle (f(a), f(b)) \in R$.

Proof: If R is an equivalence relation then T is an equivalence relation

Well if I need to prove this, I have no idea where to start. It looks pretty obvious to me that when something $\displaystyle (a,b) \in R$ with R is an equivalence relation, then T is also an equivalence relation?

If not, can someone show me how to start? How to approach this problem?

Thanks!