Write out relation from a function

Question

I have this problem: "Let $R$ be a binary relation $(x,y)\in R$ if and only if $f(x) = f(y)$

where $f: \{a, b, c, d\} \rightarrow \{0, 1\}$ given by $f(a) = 0$, $f(b) = 1$, $f(c) = 0$, $f(d) = 0$

Write out $R$ and show that it's an equivalence relation."

I can't seem to grasp this particular question. Particularly the part about $f(x) = f(y)$

I know that it has $R$ has to be reflexive, symmetric and transitive for it to be an equivalence relation, but I guess I'm having trouble seeing exactly what's in $R$. I know it's supposed to be a subset of $\{a, b, c, d\}\times\{0, 1\}$, but the restriction $f(x) = f(y)$ is confusing me. Wondered if someone could explain?

Answer 1

R = {(a,c), (c,a), (a,d), (d,a), (d,c), (c,d), (a,a), (c,c), (d,d), (b,b)}

Hope that helps.

Note: The claim that R should be a subset of {a,b,c,d}x{0,1} is incorrect.