How to prove a relation is reflexive and transitive. [closed]

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In a question paper (I downloaded from internet) there was a question,

Let $f\colon A\to B$ be a function. Define $$R := \bigl\{\left(a,b\right) \mid \text{$a,b \in A$ and $f(a)=f(b)$}\bigr\}.$$ Show that $R$ is reflexive and transitive.

How can I solve this problem? Please help me.

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1 Answer

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Huge hint:

Reflexive: For each $a\in A$, $f\left(a\right)=f\left(a\right)$ and hence $\left(a,a\right)$ is in $R$.

Transitive: Suppose $\left(a,b\right),\left(b,c\right)\in R$. Then $f\left(a\right)=f\left(b\right)$ and $f\left(b\right)=f\left(c\right)$ so that $f\left(a\right)=f\left(c\right)$ and hence __.

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